Thomas Bayes

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The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy by Sharon Bertsch McGrayne

Abraham Wald, Alan Greenspan, Bayesian statistics, bioinformatics, Bletchley Park, British Empire, classic study, Claude Shannon: information theory, Daniel Kahneman / Amos Tversky, data science, double helix, Dr. Strangelove, driverless car, Edmond Halley, Fellow of the Royal Society, full text search, government statistician, Henri Poincaré, Higgs boson, industrial research laboratory, Isaac Newton, Johannes Kepler, John Markoff, John Nash: game theory, John von Neumann, linear programming, longitudinal study, machine readable, machine translation, meta-analysis, Nate Silver, p-value, Pierre-Simon Laplace, placebo effect, prediction markets, RAND corporation, recommendation engine, Renaissance Technologies, Richard Feynman, Richard Feynman: Challenger O-ring, Robert Mercer, Ronald Reagan, seminal paper, speech recognition, statistical model, stochastic process, Suez canal 1869, Teledyne, the long tail, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, Turing machine, Turing test, uranium enrichment, We are all Keynesians now, Yom Kippur War

Price, in a letter to John Canton, A.M.F.R.S. A letter from the late Reverend Mr. Thomas Bayes, F.R.S., to John Canton, M.A. and F.R.S. Author(s): Mr. Bayes and Mr. Price. Philosophical Transactions (1683–1775) (53) 370–418. Royal Society. The original Bayes–Price article. Bebb, ED. (1935) Nonconformity and Social and Economic Life 1660–1800. London: Epworth Press. Bellhouse, David R. (2002) On some recently discovered manuscripts of Thomas Bayes. Historia Mathematica (29) 383–94. ———. (2007a) The Reverend Thomas Bayes, FRS: A biography to celebrate the tercentenary of his birth. Statistical Science (19:1) 3–43.

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University of Kentucky Press. Dale, Andrew I. (1988) On Bayes’ theorem and the inverse Bernoulli theorem. Historia Mathematica (15) 348–60. ———. (1991) Thomas Bayes’s work on infinite series. Historia Mathematica (18) 312–27. ———. (1999) A History of Inverse Probability from Thomas Bayes to Karl Pearson. 2d ed. Springer. One of the foundational works in the history of probability. ———. (2003) Most Honourable Remembrance: The Life and Work of Thomas Bayes. Springer. With Bellhouse, the main source for Bayes’ life. Daston, Lorraine. (1988) Classical Probability in the Enlightenment. Princeton University Press.

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The degraded condition of his vault may have contributed to the confusion. Second, the often-reproduced portrait of Thomas Bayes is almost assuredly of someone else named “T. Bayes.” The sketch first appeared in 1936 in History of Life Insurance in its Formative Years by Terence O’Donnell. However, the picture’s caption on page 335 says it is of “Rev. T. Bayes, Improver of the Columnar Method developed by Barrett,” and Barrett did not develop his method until 1810, a half-century after the death of “our” Rev. Thomas Bayes. Bellhouse (2004) first noticed that the portrait’s hairstyle is anachronistic. Sharon North, curator of Textiles and Fashion at the Victoria and Albert Museum, London, agrees: “The hairstyle in this portrait looks very 20th century. . . .

The Doomsday Calculation: How an Equation That Predicts the Future Is Transforming Everything We Know About Life and the Universe by William Poundstone

Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, Arthur Eddington, Bayesian statistics, behavioural economics, Benoit Mandelbrot, Berlin Wall, bitcoin, Black Swan, conceptual framework, cosmic microwave background, cosmological constant, cosmological principle, CRISPR, cuban missile crisis, dark matter, DeepMind, digital map, discounted cash flows, Donald Trump, Doomsday Clock, double helix, Dr. Strangelove, Eddington experiment, Elon Musk, Geoffrey Hinton, Gerolamo Cardano, Hans Moravec, heat death of the universe, Higgs boson, if you see hoof prints, think horses—not zebras, index fund, Isaac Newton, Jaron Lanier, Jeff Bezos, John Markoff, John von Neumann, Large Hadron Collider, mandelbrot fractal, Mark Zuckerberg, Mars Rover, Neil Armstrong, Nick Bostrom, OpenAI, paperclip maximiser, Peter Thiel, Pierre-Simon Laplace, Plato's cave, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, ride hailing / ride sharing, Rodney Brooks, Ronald Reagan, Ronald Reagan: Tear down this wall, Sam Altman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, self-driving car, Silicon Valley, Skype, Stanislav Petrov, Stephen Hawking, strong AI, tech billionaire, Thomas Bayes, Thomas Malthus, time value of money, Turing test

Since the 1940s, “Disgusted of Tunbridge Wells” has been a facetious pseudonym for letters to the editor expressing stodgy views. Tunbridge Wells was nonetheless the birthplace of one of the contemporary world’s most disruptive ideas. Not many traces remain of the town’s onetime minister Thomas Bayes (1701–1761). The Bayes family had made its fortune several generations earlier, in the cutlery business of Sheffield. Thomas Bayes studied theology and logic at the University of Edinburgh. After several years in London, he moved to Tunbridge Wells in 1733 or 1734 and became minister of Mount Sion Chapel. Bayes was a Presbyterian nonconformist, opposing the Church of England and the Book of Common Prayer on grounds vague to nearly all of today’s Presbyterians.

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This bomb broke apart, and the fragments fell into a swampy area with enough water to soften the impact and spare the conventional explosives. Bomb disposal expert Lieutenant Jack ReVelle was called in to find the pieces. “Until my death,” ReVelle said, “I will never forget hearing my sergeant say, ‘Lieutenant, we found the arm/safe switch.’ And I said, ‘Great.’ He said, ‘Not great. It’s on “arm.”’” “You’re the Product” Thomas Bayes, the nonconformist minister of Tunbridge Wells, England, drew his last breath on April 17, 1761. For reasons not clear he left his life’s greatest achievement filed away, unpublished and unread. It was another mathematically inclined minister, Richard Price, who found Bayes’s manuscript after his death and recognized its importance.

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Round the decay Of that colossal Wreck, boundless and bare The lone and level sands stretch far away.” This is the sonnet “Ozymandias” (1818) by Romantic poet Percy Bysshe Shelley, husband of Frankenstein author Mary Shelley, daughter of feminist Mary Wollstonecraft, friend of minister Richard Price, promoter of the intellectual property of Thomas Bayes. The theme of “Ozymandias” is that glory is fleeting. Nothing lasts. In the summer of 1969, J. Richard Gott III celebrated his Harvard graduation with a tour of Europe. He visited the supreme monument of Cold War anxiety, the Berlin Wall. Standing in the shadow of the landmark, he contemplated its history and future.

The Laws of Medicine: Field Notes From an Uncertain Science by Siddhartha Mukherjee

Atul Gawande, cognitive dissonance, Johannes Kepler, medical residency, randomized controlled trial, retrograde motion, stem cell, TED Talk, Thomas Bayes

Thank you for downloading this TED Books eBook. * * * Join our mailing list and get updates on new releases, deals, bonus content and other great books from TED Books and Simon & Schuster. CLICK HERE TO SIGN UP or visit us online to sign up at eBookNews.SimonandSchuster.com To Thomas Bayes (1702–1761), who saw uncertainty with such certainty “Are you planning to follow a career in Magical Laws, Miss Granger?” asked Scrimgeour. “No, I’m not,” retorted Hermione. “I’m hoping to do some good in the world!” J. K. Rowling The learned men of former ages employed a great part of their time and thoughts searching out the hidden causes of distemper, were curious in imagining the secret workmanship of nature and . . . putting all these fancies together, fashioned to themselves systems and hypotheses [that] diverted their enquiries from the true and advantageous knowledge of things.

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The core logic holds true whether you are trying to forecast tomorrow’s weather or seeking to predict rises and falls in the stock market. It is a universal feature of all tests. .... The man responsible for this strange and illuminating idea was neither a doctor nor a scientist by trade. Born in Hertfordshire in 1702, Thomas Bayes was a clergyman and philosopher who served as the minister at the chapel in Tunbridge Wells, near London. He published only two significant papers in his lifetime—the first, a defense of God, and the second, a defense of Newton’s theory of calculus (it was a sign of the times that in 1732, a clergyman found no cognitive dissonance between these two efforts).

The Book of Why: The New Science of Cause and Effect by Judea Pearl, Dana Mackenzie

affirmative action, Albert Einstein, AlphaGo, Asilomar, Bayesian statistics, computer age, computer vision, Computing Machinery and Intelligence, confounding variable, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, data science, deep learning, DeepMind, driverless car, Edmond Halley, Elon Musk, en.wikipedia.org, experimental subject, Great Leap Forward, Gregor Mendel, Isaac Newton, iterative process, John Snow's cholera map, Loebner Prize, loose coupling, Louis Pasteur, Menlo Park, Monty Hall problem, pattern recognition, Paul Erdős, personalized medicine, Pierre-Simon Laplace, placebo effect, Plato's cave, prisoner's dilemma, probability theory / Blaise Pascal / Pierre de Fermat, randomized controlled trial, Recombinant DNA, selection bias, self-driving car, seminal paper, Silicon Valley, speech recognition, statistical model, Stephen Hawking, Steve Jobs, strong AI, The Design of Experiments, the scientific method, Thomas Bayes, Turing test

REVEREND BAYES AND THE PROBLEM OF INVERSE PROBABILITY Thomas Bayes, after whom I named the networks in 1985, never dreamed that a formula he derived in the 1750s would one day be used to identify disaster victims. He was concerned only with the probabilities of two events, one (the hypothesis) occurring before the other (the evidence). Nevertheless, causality was very much on his mind. In fact, causal aspirations were the driving force behind his analysis of “inverse probability.” A Presbyterian minister who lived from 1702 to 1761, the Reverend Thomas Bayes appears to have been a mathematics geek. As a dissenter from the Church of England, he could not study at Oxford or Cambridge and was educated instead at the University of Scotland, where he likely picked up quite a bit of math.

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(Twenty years earlier, theologian Thomas Woolston had gone to prison for blasphemy for writing such things.) Hume’s main point was that inherently fallible evidence cannot overrule a proposition with the force of natural law, such as “Dead people stay dead.” FIGURE 3.1. Title page of the journal where Thomas Bayes’s posthumous article on inverse probability was published and the first page of Richard Price’s introduction. For Bayes, this assertion provoked a natural, one might say Holmesian question: How much evidence would it take to convince us that something we consider improbable has actually happened?

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If we know the length of the table and it is perfectly smooth and flat, this is a very easy question (Figure 3.2, top). For example, on a twelve-foot snooker table, the probability of the ball stopping within a foot of the end would be 1/12. On an eight-foot billiard table, the probability would be 1/8. FIGURE 3.2. Thomas Bayes’s pool table example. In the first version, a forward-probability question, we know the length of the table and want to calculate the probability of the ball stopping within x feet of the end. In the second, an inverse-probability question, we observe that the ball stopped x feet from the end and want to estimate the likelihood that the table’s length is L.

Life Is Simple by Johnjoe McFadden

Albert Einstein, Albert Michelson, Alfred Russel Wallace, animal electricity, anthropic principle, Astronomia nova, Bayesian statistics, Brownian motion, Commentariolus, complexity theory, cosmic microwave background, cosmological constant, cosmological principle, COVID-19, dark matter, double helix, Edmond Halley, en.wikipedia.org, epigenetics, Ernest Rutherford, Fellow of the Royal Society, gentleman farmer, Gregor Mendel, Henri Poincaré, Higgs boson, horn antenna, invention of the printing press, Isaac Newton, James Watt: steam engine, Johann Wolfgang von Goethe, Johannes Kepler, lockdown, music of the spheres, On the Revolutions of the Heavenly Spheres, Plato's cave, retrograde motion, Richard Feynman, the scientific method, Thomas Bayes, Thomas Malthus, William of Occam

Bertrand Russell, 19141 In April 1761, thirty-four years after the death of Isaac Newton and 118 years before the birth of Albert Einstein, Richard Price (1723–91), the non-conformist Protestant minister, moral philosopher and mathematician, examined the unpublished papers of his recently deceased friend and mathematician Thomas Bayes (1702–61). Bayes had been a modestly successful scientist. Thirty years earlier, he had rushed to the defence of Isaac Newton’s mathematical method known as calculus, which had been attacked in an article addressed to ‘an infidel mathematician’ by the Irish philosopher and Roman Catholic bishop George Berkeley who feared that Newton’s mechanistic science would undermine religious faith.

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Chance, or probability, was a hot topic in the eighteenth century as the insurance business in England and Scotland had made a fortune on its ability to put a price on the risk of death, shipwreck, damage, illness, injury or any misfortune. Several of Price’s family were actuaries and, ten years later, he would write his own book on statistical approaches to actuarial calculations. However, in 1761, he had never seen anything like the statistics described in Bayes’s paper. Thomas Bayes is one of the most elusive heroes of our story. We hardly know him any better than we do William of Occam. There is a widely used portrait of a rather stern dark-haired man in clerical gown and collar that is often claimed to be of Bayes, yet the attribution is, at best, doubtful.2 He was born in 1702, probably in Hertfordshire, the son of another non-conformist minister, Joshua Bayes.

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However, the town had thereafter earned something of a salacious reputation and, in his The Debt to Pleasure3 published in 1685, John Wilmot, Earl of Rochester had described it as ‘The Rendevouz of Fooles, Buffoones, and Praters/ Cuckolds, Whores, Citizens, their Wives and Daughters’. The Reverend Thomas Bayes was not a particularly popular preacher in the ‘Rendevous of Fooles’, but he did establish a reputation as a scholar and was even invited to demonstrate the melting of ice to ‘Three Natives of the East Indies’ who visited in 1740. Probably because of his defence of Newton’s calculus, Bayes was elected to the Royal Society in 1742, but published no further mathematical work before his death in 1761.

The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow

Albert Einstein, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Atul Gawande, behavioural economics, Brownian motion, butterfly effect, correlation coefficient, Daniel Kahneman / Amos Tversky, data science, Donald Trump, feminist movement, forensic accounting, Gary Kildall, Gerolamo Cardano, Henri Poincaré, index fund, Isaac Newton, law of one price, Monty Hall problem, pattern recognition, Paul Erdős, Pepto Bismol, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, Ronald Reagan, Stephen Hawking, Steve Jobs, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, V2 rocket, Watson beat the top human players on Jeopardy!

One of the paranoid delusions the former employer’s psychiatrist pointed to was the student’s alleged invention of a fictitious eighteenth-century minister. In particular, the psychiatrist scoffed at the student’s claim that this minister was an amateur mathematician who had created in his spare moments a bizarre theory of probability. The minister’s name, according to the student, was Thomas Bayes. His theory, the student asserted, described how to assess the chances that some event would occur if some other event also occurred. What are the chances that a particular student would be the subject of a vast secret conspiracy of experimental psychologists? Admittedly not huge. But what if one’s wife speaks one’s thoughts before one can utter them and co-workers foretell your professional fate over drinks in casual conversation?

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And he presented the court with a mumbo jumbo of formulas and calculations regarding his hypothesis, concluding that the additional evidence meant that the probability was 999,999 in 1 million that he was right about the conspiracy. The enemy psychiatrist claimed that this mathematician-minister and his theory were figments of the student’s schizophrenic imagination. The student asked the professor to help him refute that claim. The professor agreed. He had good reason, for Thomas Bayes, born in London in 1701, really was a minister, with a parish at Tunbridge Wells. He died in 1761 and was buried in a park in London called Bunhill Fields, in the same grave as his father, Joshua, also a minister. And he indeed did invent a theory of “conditional probability” to show how the theory of probability can be extended from independent events to events whose outcomes are connected.

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The sad part of this story is not just the middle-aged schizophrenic himself, but the medical and legal team on the other side. It is unfortunate that some people suffer from schizophrenia, but even though drugs can help to mediate the illness, they cannot battle ignorance. And ignorance of the ideas of Thomas Bayes, as we shall see, resides at the heart of many serious mistakes in both medical diagnosis and legal judgment. It is an ignorance that is rarely addressed during a doctor’s or a lawyer’s professional training. We also make Bayesian judgments in our daily lives. A film tells the story of an attorney who has a great job, a charming wife, and a wonderful family.

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths

4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, algorithmic bias, algorithmic trading, anthropic principle, asset allocation, autonomous vehicles, Bayesian statistics, behavioural economics, Berlin Wall, Big Tech, Bill Duvall, bitcoin, Boeing 747, Charles Babbage, cognitive load, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, data science, David Heinemeier Hansson, David Sedaris, delayed gratification, dematerialisation, diversification, Donald Knuth, Donald Shoup, double helix, Dutch auction, Elon Musk, exponential backoff, fault tolerance, Fellow of the Royal Society, Firefox, first-price auction, Flash crash, Frederick Winslow Taylor, fulfillment center, Garrett Hardin, Geoffrey Hinton, George Akerlof, global supply chain, Google Chrome, heat death of the universe, Henri Poincaré, information retrieval, Internet Archive, Jeff Bezos, Johannes Kepler, John Nash: game theory, John von Neumann, Kickstarter, knapsack problem, Lao Tzu, Leonard Kleinrock, level 1 cache, linear programming, martingale, multi-armed bandit, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, Pierre-Simon Laplace, power law, prediction markets, race to the bottom, RAND corporation, RFC: Request For Comment, Robert X Cringely, Sam Altman, scientific management, sealed-bid auction, second-price auction, self-driving car, Silicon Valley, Skype, sorting algorithm, spectrum auction, Stanford marshmallow experiment, Steve Jobs, stochastic process, Thomas Bayes, Thomas Malthus, Tragedy of the Commons, traveling salesman, Turing machine, urban planning, Vickrey auction, Vilfredo Pareto, Walter Mischel, Y Combinator, zero-sum game

Reasoning Backward with the Reverend Bayes If we be, therefore, engaged by arguments to put trust in past experience, and make it the standard of our future judgement, these arguments must be probable only. —DAVID HUME More than 250 years ago, the question of making predictions from small data weighed heavily on the mind of the Reverend Thomas Bayes, a Presbyterian minister in the charming spa town of Tunbridge Wells, England. If we buy ten tickets for a new and unfamiliar raffle, Bayes imagined, and five of them win prizes, then it seems relatively easy to estimate the raffle’s chances of a win: 5/10, or 50%. But what if instead we buy a single ticket and it wins a prize?

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“The Unreasonable Effectiveness of Data”: The talk was derived from Halevy, Norvig, and Pereira, “The Unreasonable Effectiveness of Data.” “these arguments must be probable only”: An Enquiry Concerning Human Understanding, §IV, “Sceptical Doubts Concerning the Operations of the Understanding.” Bayes’s own history: Our brief biography draws on Dale, A History of Inverse Probability, and Bellhouse, “The Reverend Thomas Bayes.” in either 1746, ’47, ’48, or ’49: Bayes’s legendary paper, undated, had been filed between a pair of papers dated 1746 and 1749. See, e.g., McGrayne, The Theory That Would Not Die. defense of Newton’s newfangled “calculus”: An Introduction to the Doctrine of fluxions, and Defence of the Mathematicians against the Objections of the Author of the analyst, so far as they are assigned to affect their general methods of Reasoning.

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Communications of the ACM 12, no. 6 (1969): 349–353. Belew, Richard K. Finding Out About: A Cognitive Perspective on Search Engine Technology and the WWW. Cambridge, UK: Cambridge University Press, 2000. Bell, Aubrey F. G. In Portugal. New York: John Lane, 1912. Bellhouse, David R. “The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth.” Statistical Science 19 (2004): 3–43. Bellman, Richard. Dynamic Programming. Princeton, NJ: Princeton University Press, 1957. ______. “A Problem in the Sequential Design of Experiments.” Sankhyā: The Indian Journal of Statistics 16 (1956): 221–229.

The Signal and the Noise: Why So Many Predictions Fail-But Some Don't by Nate Silver

airport security, Alan Greenspan, Alvin Toffler, An Inconvenient Truth, availability heuristic, Bayesian statistics, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, big-box store, Black Monday: stock market crash in 1987, Black Swan, Boeing 747, book value, Broken windows theory, business cycle, buy and hold, Carmen Reinhart, Charles Babbage, classic study, Claude Shannon: information theory, Climategate, Climatic Research Unit, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, computer age, correlation does not imply causation, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, Daniel Kahneman / Amos Tversky, disinformation, diversification, Donald Trump, Edmond Halley, Edward Lorenz: Chaos theory, en.wikipedia.org, equity premium, Eugene Fama: efficient market hypothesis, everywhere but in the productivity statistics, fear of failure, Fellow of the Royal Society, Ford Model T, Freestyle chess, fudge factor, Future Shock, George Akerlof, global pandemic, Goodhart's law, haute cuisine, Henri Poincaré, high batting average, housing crisis, income per capita, index fund, information asymmetry, Intergovernmental Panel on Climate Change (IPCC), Internet Archive, invention of the printing press, invisible hand, Isaac Newton, James Watt: steam engine, Japanese asset price bubble, John Bogle, John Nash: game theory, John von Neumann, Kenneth Rogoff, knowledge economy, Laplace demon, locking in a profit, Loma Prieta earthquake, market bubble, Mikhail Gorbachev, Moneyball by Michael Lewis explains big data, Monroe Doctrine, mortgage debt, Nate Silver, negative equity, new economy, Norbert Wiener, Oklahoma City bombing, PageRank, pattern recognition, pets.com, Phillips curve, Pierre-Simon Laplace, Plato's cave, power law, prediction markets, Productivity paradox, proprietary trading, public intellectual, random walk, Richard Thaler, Robert Shiller, Robert Solow, Rodney Brooks, Ronald Reagan, Saturday Night Live, savings glut, security theater, short selling, SimCity, Skype, statistical model, Steven Pinker, The Great Moderation, The Market for Lemons, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, Timothy McVeigh, too big to fail, transaction costs, transfer pricing, University of East Anglia, Watson beat the top human players on Jeopardy!, Wayback Machine, wikimedia commons

The key is in determining whether the patterns represent noise or signal. But although there isn’t any one particular key to why Voulgaris might or might not bet on a given game, there is a particular type of thought process that helps govern his decisions. It is called Bayesian reasoning. The Improbable Legacy of Thomas Bayes Thomas Bayes was an English minister who was probably born in 1701—although it may have been 1702. Very little is certain about Bayes’s life, even though he lent his name to an entire branch of statistics and perhaps its most famous theorem. It is not even clear that anybody knows what Bayes looked like; the portrait of him that is commonly used in encyclopedia articles may have been misattributed.19 What is in relatively little dispute is that Bayes was born into a wealthy family, possibly in the southeastern English county of Hertfordshire.

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That works out to 150 such streaks per season between the thirty NBA teams combined. 19. D. R. Bellhouse, “The Reverend Thomas Bayes FRS: A Biography to Celebrate the Tercentenary of His Birth,” Statistical Science, 19, 1, pp. 3–43; 2004. http://www2.isye.gatech.edu/~brani/isyebayes/bank/bayesbiog.pdf. 20. Bayes may also have been an Arian, meaning someone who followed the teachings of the early Christian leader Arias and who regarded Jesus Christ as the divine son of God rather than (as most Christians then and now believe) a direct manifestation of God. 21. Thomas Bayes, “Divine Benevolence: Or an Attempt to Prove That the Principal End of the Divine Providence and Government Is the Happiness of His Creatures.” http://archive.org/details/DivineBenevolenceOrAnAttemptToProveThatThe. 22.

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There are many reasons for it—some having to do with our psychological biases, some having to do with common methodological errors, and some having to do with misaligned incentives. Close to the root of the problem, however, is a flawed type of statistical thinking that these researchers are applying. FIGURE 8-6: A GRAPHICAL REPRESENTATION OF FALSE POSITIVES When Statistics Backtracked from Bayes Perhaps the chief intellectual rival to Thomas Bayes—although he was born in 1890, almost 120 years after Bayes’s death—was an English statistician and biologist named Ronald Aylmer (R. A.) Fisher. Fisher was a much more colorful character than Bayes, almost in the English intellectual tradition of Christopher Hitchens. He was handsome but a slovenly dresser,42 always smoking his pipe or his cigarettes, constantly picking fights with his real and imagined rivals.

The Art of Statistics: Learning From Data by David Spiegelhalter

Abraham Wald, algorithmic bias, Anthropocene, Antoine Gombaud: Chevalier de Méré, Bayesian statistics, Brexit referendum, Carmen Reinhart, Charles Babbage, complexity theory, computer vision, confounding variable, correlation coefficient, correlation does not imply causation, dark matter, data science, deep learning, DeepMind, Edmond Halley, Estimating the Reproducibility of Psychological Science, government statistician, Gregor Mendel, Hans Rosling, Higgs boson, Kenneth Rogoff, meta-analysis, Nate Silver, Netflix Prize, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, p-value, placebo effect, probability theory / Blaise Pascal / Pierre de Fermat, publication bias, randomized controlled trial, recommendation engine, replication crisis, self-driving car, seminal paper, sparse data, speech recognition, statistical model, sugar pill, systematic bias, TED Talk, The Design of Experiments, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Malthus, Two Sigma

This has only come to prominence in the last fifty years, but its basic principles go back somewhat further, in fact to the Reverend Thomas Bayes, a Nonconformist minister turned probability theorist and philosopher from Tunbridge Wells, who died in 1761.fn1 The good news is that the Bayesian approach opens fine new possibilities for making the most of complex data. The bad news is that it means putting aside almost everything you may have learned in this book and elsewhere about estimation, confidence intervals, P-values, hypothesis testing, and so on. What Is the Bayesian Approach? Thomas Bayes’ first great contribution was to use probability as an expression of our lack of knowledge about the world or, equivalently, our ignorance about what is currently going on.

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Expected frequencies make Bayesian analysis reasonably straightforward for simple situations that involve only two hypotheses, say about whether someone does or does not have a disease, or has or has not committed an offence. However, things get trickier when we want to apply the same ideas to drawing inferences about unknown quantities that might take on a range of values, such as parameters in statistical models. The Reverend Thomas Bayes’ original paper in 1763 set out to answer a very basic question of this nature: given something has happened or not happened on a known number of similar occasions, what probability should we give to it happening next time?fn4 For example, if a thumbtack has been flipped 20 times and it has come down point-up 15 times and point-down 5 times, what is the probability of it landing point-down next time?

The Art of Statistics: How to Learn From Data by David Spiegelhalter

Abraham Wald, algorithmic bias, Antoine Gombaud: Chevalier de Méré, Bayesian statistics, Brexit referendum, Carmen Reinhart, Charles Babbage, complexity theory, computer vision, confounding variable, correlation coefficient, correlation does not imply causation, dark matter, data science, deep learning, DeepMind, Edmond Halley, Estimating the Reproducibility of Psychological Science, government statistician, Gregor Mendel, Hans Rosling, Higgs boson, Kenneth Rogoff, meta-analysis, Nate Silver, Netflix Prize, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, p-value, placebo effect, probability theory / Blaise Pascal / Pierre de Fermat, publication bias, randomized controlled trial, recommendation engine, replication crisis, self-driving car, seminal paper, sparse data, speech recognition, statistical model, sugar pill, systematic bias, TED Talk, The Design of Experiments, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Malthus, Two Sigma

This has only come to prominence in the last fifty years, but its basic principles go back somewhat further, in fact to the Reverend Thomas Bayes, a Nonconformist minister turned probability theorist and philosopher from Tunbridge Wells, who died in 1761.* The good news is that the Bayesian approach opens fine new possibilities for making the most of complex data. The bad news is that it means putting aside almost everything you may have learned in this book and elsewhere about estimation, confidence intervals, P-values, hypothesis testing, and so on. What Is the Bayesian Approach? Thomas Bayes’ first great contribution was to use probability as an expression of our lack of knowledge about the world or, equivalently, our ignorance about what is currently going on.

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Expected frequencies make Bayesian analysis reasonably straightforward for simple situations that involve only two hypotheses, say about whether someone does or does not have a disease, or has or has not committed an offence. However, things get trickier when we want to apply the same ideas to drawing inferences about unknown quantities that might take on a range of values, such as parameters in statistical models. The Reverend Thomas Bayes’ original paper in 1763 set out to answer a very basic question of this nature: given something has happened or not happened on a known number of similar occasions, what probability should we give to it happening next time?* For example, if a thumbtack has been flipped 20 times and it has come down point-up 15 times and point-down 5 times, what is the probability of it landing point-down next time?

Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein

Alan Greenspan, Albert Einstein, Alvin Roth, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Bayesian statistics, behavioural economics, Big bang: deregulation of the City of London, Bretton Woods, business cycle, buttonwood tree, buy and hold, capital asset pricing model, cognitive dissonance, computerized trading, Daniel Kahneman / Amos Tversky, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Lloyd's coffeehouse, endowment effect, experimental economics, fear of failure, Fellow of the Royal Society, Fermat's Last Theorem, financial deregulation, financial engineering, financial innovation, full employment, Great Leap Forward, index fund, invention of movable type, Isaac Newton, John Nash: game theory, John von Neumann, Kenneth Arrow, linear programming, loss aversion, Louis Bachelier, mental accounting, moral hazard, Myron Scholes, Nash equilibrium, Norman Macrae, Paul Samuelson, Philip Mirowski, Post-Keynesian economics, probability theory / Blaise Pascal / Pierre de Fermat, prudent man rule, random walk, Richard Thaler, Robert Shiller, Robert Solow, spectrum auction, statistical model, stocks for the long run, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, Thomas Bayes, trade route, transaction costs, tulip mania, Vanguard fund, zero-sum game

With that innocent-sounding assertion, Bernoulli explained why King Midas was an unhappy man, why people tend to be risk-averse, and why prices must fall if customers are to be persuaded to buy more. Bernoulli's statement stood as the dominant paradigm of rational behavior for the next 250 years and laid the groundwork for modern principles of investment management. Almost exactly one hundred years after the collaboration between Pascal and Fermat, a dissident English minister named Thomas Bayes made a striking advance in statistics by demonstrating how to make better-informed decisions by mathematically blending new information into old information. Bayes's theorem focuses on the frequent occasions when we have sound intuitive judgments about the probability of some event and want to understand how to alter those judgments as actual events unfold.

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Questions put in this manner form the subject matter of what is known as inverse probability: with 12 defective pins out of 100,000, what is the probability that the true average ratio of defectives to the total is 0.01%? One of the most effective treatments of such questions was proposed by a minister named Thomas Bayes, who was born in 1701 and lived in Kent." Bayes was a Nonconformist; he rejected most of the ceremonial rituals that the Church of England had retained from the Catholic Church after their separation in the time of Henry VIII. Not much is known about Bayes, even though he was a Fellow of the Royal Society.

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The most exciting feature of all the achievements mentioned in this chapter is the daring idea that uncertainty can be measured. Uncertainty means unknown probabilities; to reverse Hacking's description of certainty, we can say that something is uncertain when our information is correct and an event fails to happen, or when our information is incorrect and an event does happen. Jacob Bernoulli, Abraham de Moivre, and Thomas Bayes showed how to infer previously unknown probabilities from the empirical facts of reality. These accomplishments are impressive for the sheer mental agility demanded, and audacious for their bold attack on the unknown. When de Moivre invoked ORIGINAL DESIGN, he made no secret of his wonderment at his own accomplishments.

Mastering Pandas by Femi Anthony

Amazon Web Services, Bayesian statistics, correlation coefficient, correlation does not imply causation, data science, Debian, en.wikipedia.org, Internet of things, Large Hadron Collider, natural language processing, p-value, power law, random walk, side project, sparse data, statistical model, Thomas Bayes

The various topics that will be discussed are as follows: Introduction to Bayesian statistics Mathematical framework for Bayesian statistics Probability distributions Bayesian versus Frequentist statistics Introduction to PyMC and Monte Carlo simulation Illustration of Bayesian inference – Switchpoint detection Introduction to Bayesian statistics The field of Bayesian statistics is built on the work of Reverend Thomas Bayes, an 18th century statistician, philosopher, and Presbyterian minister. His famous Bayes' theorem, which forms the theoretical underpinnings for Bayesian statistics, was published posthumously in 1763 as a solution to the problem of inverse probability. For more details on this topic, refer to http://en.wikipedia.org/wiki/Thomas_Bayes. Inverse probability problems were all the rage in the early 18th century and were often formulated as follows: Suppose you play a game with a friend.

How Many Friends Does One Person Need? Dunbar’s Number and Other Evolutionary Quirks by Robin Dunbar, Robin Ian MacDonald Dunbar

agricultural Revolution, Albert Michelson, Donner party, Fellow of the Royal Society, glass ceiling, Gregor Mendel, Isaac Newton, mass immigration, Nash equilibrium, nuclear winter, out of africa, pattern recognition, Richard Feynman, social intelligence, Steven Pinker, theory of mind, Thomas Bayes, Thomas Malthus, trolley problem, University of East Anglia, upwardly mobile

In 1764, the Reverend Thomas Bayes, an English Presbyterian minister and Fellow of the Royal Society, published a posthumous paper in which he sketched out a theory of probability based on confidence. It was an elegantly simple theory based on a single mathematical theorem that could be applied under any circumstances. But later mathematicians baulked at his ideas, preferring something that was more firmly rooted in observable facts: they argued that probability is better defined as something about the frequencies with which events (such as tosses of a coin) happen. Thomas Bayes and his theorem fell into obscurity.

Immortality, Inc. by Chip Walter

23andMe, Airbnb, Albert Einstein, Arthur D. Levinson, bioinformatics, Buckminster Fuller, cloud computing, CRISPR, data science, disintermediation, double helix, Elon Musk, Isaac Newton, Jeff Bezos, Larry Ellison, Law of Accelerating Returns, life extension, Menlo Park, microbiome, mouse model, pattern recognition, Peter Thiel, phenotype, radical life extension, Ray Kurzweil, Recombinant DNA, Rodney Brooks, self-driving car, Silicon Valley, Silicon Valley startup, Snapchat, South China Sea, SpaceShipOne, speech recognition, statistical model, stem cell, Stephen Hawking, Steve Jobs, TED Talk, Thomas Bayes, zero day

There could be no doubt: Smart machines was where the end of The End lay. 27 | THE NEW ORACLES In early 2016, when she became Calico Labs’ chief computing officer, the views and aspirations of Raymond Kurzweil did not inhabit the mind of Daphne Koller. This wasn’t because she shunned Kurzweil, or digits, algorithms, or computer code; far from it. She loved them all. It was just that Kurzweil wasn’t her favorite when it came to the stratagems of machine learning and artificial intelligence. Bridge Four wasn’t her thing. Her inspiration was Thomas Bayes, an 18th-century mathematician and Presbyterian minister. She had explored his work and theories in the 1990s, and then used them to develop some of the most advanced artificial intelligence algorithms in the world. Before joining Calico, Koller knew she could write her own ticket at any of Silicon Valley’s great Cloud makers: Google, Facebook, Apple.

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But did she really want to create software that made better Twitter feeds, or cool faces on Snapchat, or yet another product that piled up more of the planet’s digital ad revenues? In the sprawling world of Google, she would be a blip: one more very smart human in a sea of geeks. But Calico was different. She had never forgotten Steve Jobs’s grand goal: “Make a dent in the universe.” At Calico, maybe she could make a dent—save lives, perhaps millions—even her own. Thomas Bayes would have appreciated Koller’s interest in saving lives, being both a Presbyterian minister and a devoted supporter of the humanist philosophies that called for the rational improvement of the human race—also the foundation of transhumanism. The mathematician’s work had been largely forgotten when Koller first began exploring it.

Radical Uncertainty: Decision-Making for an Unknowable Future by Mervyn King, John Kay

Airbus A320, Alan Greenspan, Albert Einstein, Albert Michelson, algorithmic trading, anti-fragile, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, autonomous vehicles, availability heuristic, banking crisis, Barry Marshall: ulcers, battle of ideas, Bear Stearns, behavioural economics, Benoit Mandelbrot, bitcoin, Black Swan, Boeing 737 MAX, Bonfire of the Vanities, Brexit referendum, Brownian motion, business cycle, business process, capital asset pricing model, central bank independence, collapse of Lehman Brothers, correlation does not imply causation, credit crunch, cryptocurrency, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, DeepMind, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, Donald Trump, Dutch auction, easy for humans, difficult for computers, eat what you kill, Eddington experiment, Edmond Halley, Edward Lloyd's coffeehouse, Edward Thorp, Elon Musk, Ethereum, Eugene Fama: efficient market hypothesis, experimental economics, experimental subject, fear of failure, feminist movement, financial deregulation, George Akerlof, germ theory of disease, Goodhart's law, Hans Rosling, Helicobacter pylori, high-speed rail, Ignaz Semmelweis: hand washing, income per capita, incomplete markets, inflation targeting, information asymmetry, invention of the wheel, invisible hand, Jeff Bezos, Jim Simons, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Snow's cholera map, John von Neumann, Kenneth Arrow, Kōnosuke Matsushita, Linda problem, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, market bubble, market fundamentalism, military-industrial complex, Money creation, Moneyball by Michael Lewis explains big data, Monty Hall problem, Nash equilibrium, Nate Silver, new economy, Nick Leeson, Northern Rock, nudge theory, oil shock, PalmPilot, Paul Samuelson, peak oil, Peter Thiel, Philip Mirowski, Phillips curve, Pierre-Simon Laplace, popular electronics, power law, price mechanism, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, railway mania, RAND corporation, reality distortion field, rent-seeking, Richard Feynman, Richard Thaler, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Solow, Ronald Coase, sealed-bid auction, shareholder value, Silicon Valley, Simon Kuznets, Socratic dialogue, South Sea Bubble, spectrum auction, Steve Ballmer, Steve Jobs, Steve Wozniak, Suez crisis 1956, Tacoma Narrows Bridge, Thales and the olive presses, Thales of Miletus, The Chicago School, the map is not the territory, The Market for Lemons, The Nature of the Firm, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, Thomas Davenport, Thomas Malthus, Toyota Production System, transaction costs, ultimatum game, urban planning, value at risk, world market for maybe five computers, World Values Survey, Yom Kippur War, zero-sum game

But if there were to be only five games, the Marquis would certainly have lost – the result of the fifth game would be irrelevant, and it might not even have been played. It pays to go Bayes The final step in the development of the new theory of probability was the achievement of an unlikely hero – an obscure eighteenth-century country Presbyterian clergyman in England. The Reverend Thomas Bayes is by chance buried in what is now the centre of London’s financial district. Among his papers he left a theorem that is one of the most widely taught ideas in statistics today. 13 Unknown in life Bayes may have been, but his name is known today throughout the world with branches of statistics and economics named after him.

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And it is the pervasive nature of radical uncertainty which is the source of the problem. 20 THE USE AND MISUSE OF MODELS Any business craving of the leader, however foolish, will be quickly supported by detailed rates of return and strategic studies prepared by his troops. —WARREN BUFFETT 1 I n the eighteenth century there were country clergymen of exceptional intelligence who had time on their hands. They benefited from a secure reference narrative. Thomas Bayes was one; Thomas Malthus another. In 1798, Malthus set out what might be regarded as the first growth model in economics. He hypothesised that population tended to grow exponentially, as a result of what he coyly termed ‘the passions’, while food supplies could grow only linearly. The rising population would put pressure on food supplies, and then the resulting destitution would reduce that population.

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The model of the lone entrepreneur – the poor boy with a brilliant business idea who rises single-handedly from poverty; the isolated scholar scribbling brilliant ideas in a garret or country vicarage – is largely mythological. There are contrary examples. Thomas Edison was fired from the only two jobs he held, the first as telegraph boy for Western Electric and the other as CEO of the corporation which is now General Electric. The Reverend Thomas Bayes died unknown. But such examples are few, and to find them we have to go some way back in history. The most common profile of the successful entrepreneur today is the individual who draws on his or her past experience in a larger organisation, and works from inception with a team of like-minded individuals.

We Are Data: Algorithms and the Making of Our Digital Selves by John Cheney-Lippold

algorithmic bias, bioinformatics, business logic, Cass Sunstein, centre right, computer vision, critical race theory, dark matter, data science, digital capitalism, drone strike, Edward Snowden, Evgeny Morozov, Filter Bubble, Google Chrome, Google Earth, Hans Moravec, Ian Bogost, informal economy, iterative process, James Bridle, Jaron Lanier, Julian Assange, Kevin Kelly, late capitalism, Laura Poitras, lifelogging, Lyft, machine readable, machine translation, Mark Zuckerberg, Marshall McLuhan, mass incarceration, Mercator projection, meta-analysis, Nick Bostrom, Norbert Wiener, offshore financial centre, pattern recognition, price discrimination, RAND corporation, Ray Kurzweil, Richard Thaler, ride hailing / ride sharing, Rosa Parks, Silicon Valley, Silicon Valley startup, Skype, Snapchat, software studies, statistical model, Steven Levy, technological singularity, technoutopianism, the scientific method, Thomas Bayes, Toyota Production System, Turing machine, uber lyft, web application, WikiLeaks, Zimmermann PGP

A composite Quantcast image from a 2008 methodology white paper explains how its ‘gender’ inference model works across websites. Source: Quantcast, “Quantcast Methodology Overview,” 2008, www.quantcast.com [no longer available]. The manner by which this model “gets smarter” is best explained by the statistical method of Bayesian probability. Thomas Bayes was an amateur mathematician whose 1763 posthumously published “Essay towards Solving a Problem in the Doctrine of Chances” asserted, among other things, a simple fact: we update a phenomenon’s meaning when new data about that phenomenon arrives.35 Media scholar Finn Brunton offers us an excellent exposition: Imagine someone new to this world seeing the first sunset of her life.

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Michael Zimmer, “The Externalities of Search 2.0: The Emerging Privacy Threats When the Drive for the Perfect Search Engine Meets Web 2.0,” First Monday 13, no. 3 (2008), http://firstmonday.org. 31. Quantcast, “Understanding Digital Audience Measurement,” 2014, www.quantcast.com. 32. Ibid. 33. Interview with anonymous data engineer, February 9, 2011. 34. Quantcast, “Quantcast Methodology Overview,” 2008, www.quantcast.com [no longer available]. 35. Thomas Bayes and Richard Price, “An Essay towards Solving a Problem in the Doctrine of Chances, by the Late Rev. Mr. Bayes, F.R.S. Communicated by Mr. Price, in a Letter to John Canton, A.M.F.R.S.,” Philosophical Transactions (1683–1775) 53 (1763): 370–418. 36. Finn Brunton, Spam: A Shadow History of the Internet (Cambridge, MA: MIT Press, 2013), 135. 37.

Being You: A New Science of Consciousness by Anil Seth

AlphaGo, artificial general intelligence, augmented reality, backpropagation, carbon-based life, Claude Shannon: information theory, computer age, computer vision, Computing Machinery and Intelligence, coronavirus, correlation does not imply causation, CRISPR, cryptocurrency, deep learning, deepfake, DeepMind, Drosophila, en.wikipedia.org, Filter Bubble, GPT-3, GPT-4, John Markoff, longitudinal study, Louis Pasteur, mirror neurons, Neil Armstrong, Nick Bostrom, Norbert Wiener, OpenAI, paperclip maximiser, pattern recognition, Paul Graham, Pierre-Simon Laplace, planetary scale, Plato's cave, precautionary principle, Ray Kurzweil, self-driving car, speech recognition, stem cell, systems thinking, technological singularity, TED Talk, telepresence, the scientific method, theory of mind, Thomas Bayes, TikTok, Turing test

C. (2018), ‘Prior object-knowledge sharpens properties of early visual feature detectors’, Scientific Reports, 8:10853. Used with permission of the authors and under a Creative Commons Attribution 4.0 International License, with thanks to Christoph Teufel. 5 The Wizard of Odds The Reverend Thomas Bayes (1702–1761) – a Presbyterian minister, philosopher, and statistician, who lived much of his life in Tunbridge Wells, in southern England – never got around to publishing the theorem that immortalised his name. His ‘Essay towards Solving a Problem in the Doctrine of Chances’ was presented to the Royal Society in London two years after his death by fellow preacher-philosopher Richard Price, and much of the mathematical heavy lifting was done later on by the French mathematician Pierre-Simon Laplace.

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— Let’s return to our imagined brain, quiet and dark inside its skull, trying to figure out what’s out there in the world. We can now recognise this challenge as an ideal opportunity to invoke Bayesian inference. When the brain is making best guesses about the causes of its noisy and ambiguous sensory signals, it is following the principles of the Reverend Thomas Bayes. Perceptual priors can be encoded at many levels of abstraction and flexibility. These range from very general and relatively fixed priors such as ‘light comes from above’ to situation-specific priors like ‘the approaching furry object is a gorilla’. Likelihoods in the brain encode mappings from potential causes to sensory signals.

Predictive Analytics: The Power to Predict Who Will Click, Buy, Lie, or Die by Eric Siegel

Alan Greenspan, Albert Einstein, algorithmic trading, Amazon Mechanical Turk, Apollo 11, Apple's 1984 Super Bowl advert, backtesting, Black Swan, book scanning, bounce rate, business intelligence, business process, butter production in bangladesh, call centre, Charles Lindbergh, commoditize, computer age, conceptual framework, correlation does not imply causation, crowdsourcing, dark matter, data is the new oil, data science, driverless car, en.wikipedia.org, Erik Brynjolfsson, Everything should be made as simple as possible, experimental subject, Google Glasses, happiness index / gross national happiness, information security, job satisfaction, Johann Wolfgang von Goethe, lifelogging, machine readable, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, mass immigration, Moneyball by Michael Lewis explains big data, Nate Silver, natural language processing, Netflix Prize, Network effects, Norbert Wiener, personalized medicine, placebo effect, prediction markets, Ray Kurzweil, recommendation engine, risk-adjusted returns, Ronald Coase, Search for Extraterrestrial Intelligence, self-driving car, sentiment analysis, Shai Danziger, software as a service, SpaceShipOne, speech recognition, statistical model, Steven Levy, supply chain finance, text mining, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Davenport, Turing test, Watson beat the top human players on Jeopardy!, X Prize, Yogi Berra, zero-sum game

The predictions were generated from machine learning across 50 million learning cases, each depicting a micro-lesson from history of the form, “User Mary was shown ad A and she did click it” (a positive case) or “User John was shown ad B and he did not click it” (a negative case). The learning technology employed to pick the best ad for each user was a Naïve Bayes model. Reverend Thomas Bayes was an eighteenth-century mathematician, and the “Naïve” part means that we take a very smart man’s ideas and compromise them in a way that simplifies yet makes their application feasible, resulting in a practical method that’s often considered good enough at prediction, and scales to the task at hand.

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Apple Mac Apple Siri Argonne National Laboratory Arizona Petrified Forest National Park Arizona State University artificial intelligence (AI) about Amazon.com Mechanical Turk mind-reading technology possibility of, the Watson computer and Asimov, Isaac astronomy AT&T Research BellKor Netflix Prize teams Australia Austria automobile insurance crashes, predicting credit scores and accidents driver inatentiveness, predicting fraud predictions for Averitt aviation incidents Aviva Insurance (UK) AWK computer language B backtesting. See also test data Baesens, Ben bagging (bootstrap aggregating) Bangladesh Barbie dolls Bayes, Thomas (Bayes Network) Beane, Billy Beano Beaux, Alex behavioral predictors Bella Pictures BellKor BellKor Netflix Prize teams Ben Gurion University (Israel) Bernstein, Peter Berra, Yogi Big Bang Theory, The Big Bang theory Big Brother BigChaos team “big data” movement billing errors, predicting black box trading Black Swan, The (Taleb) blogs and blogging anxiety, predicting from entries collective intelligence and data glut and content in LiveJournal mood prediction research via nature of Blue Cross Blue Shield of Tennessee BMW BNSF Railway board games, predictive play of Bohr, Niels book titles, testing Bowie, David brain activity, predicting Brandeis, Louis Brasil Telecom (Oi) breast cancer, predicting Brecht, Bertolt Breiman, Leo Brigham Young University British Broadcasting Corporation (BBC) Brobst, Stephen Brooks, Mel Brynjolfsson, Eric buildings, predicting fault in Bullard, Ben burglaries, predicting business rules, decision trees and buying behavior, predicting C Cage, Nicolas Canadian Automobile Association Canadian Tire car crashes and harm, predicting CareerBuilder Carlin, George Carlson, Gretchen Carnegie Mellon University CART decision trees Castagno, Davide causality cell phone industry consumer behavior and dropped calls, predicting GPS data and location predicting Telenor (Norway) CellTel (African telecom) Central Tables.

The Irrational Economist: Making Decisions in a Dangerous World by Erwann Michel-Kerjan, Paul Slovic

"World Economic Forum" Davos, Alan Greenspan, An Inconvenient Truth, Andrei Shleifer, availability heuristic, bank run, behavioural economics, Black Swan, business cycle, Cass Sunstein, classic study, clean water, cognitive dissonance, collateralized debt obligation, complexity theory, conceptual framework, corporate social responsibility, Credit Default Swap, credit default swaps / collateralized debt obligations, cross-subsidies, Daniel Kahneman / Amos Tversky, endowment effect, experimental economics, financial innovation, Fractional reserve banking, George Akerlof, hindsight bias, incomplete markets, information asymmetry, Intergovernmental Panel on Climate Change (IPCC), invisible hand, Isaac Newton, iterative process, Kenneth Arrow, Loma Prieta earthquake, London Interbank Offered Rate, market bubble, market clearing, money market fund, moral hazard, mortgage debt, Oklahoma City bombing, Pareto efficiency, Paul Samuelson, placebo effect, precautionary principle, price discrimination, price stability, RAND corporation, Richard Thaler, Robert Shiller, Robert Solow, Ronald Reagan, Savings and loan crisis, social discount rate, source of truth, statistical model, stochastic process, subprime mortgage crisis, The Wealth of Nations by Adam Smith, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transaction costs, ultimatum game, University of East Anglia, urban planning, Vilfredo Pareto

This chapter explores a two-part conjecture: (1) After the occurrence of a virgin risk, people will overestimate the probability of another occurrence in the near future; (2) by contrast, after an experienced risk occurs, people will under-update their assessment of another event occurring soon. THE INABILITY TO USE BAYESIAN UPDATING IN EVERYDAY PRACTICE Risks are often posited to have an unknown true probability. The textbook model for how to proceed employs Bayes’ Rule (after eighteenth-century British mathematician Thomas Bayes), which shows mathematically how people should rationally change their existing beliefs about something in light of new evidence. Individuals use information available beforehand to form a so-called prior belief about the probability that an event will occur in a given period. New evidence about the risk is captured in something called a likelihood function, which expresses how plausible the evidence is given each possible value of the probability.

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Anxiety Arrow, Ken Arthur Andersen Assets Asteroid and Comet Impact Hazards Group (NASA) Asteroid explosions, risk of At War with the Weather (Kunreuther and Michel-Kerjan) Attention deficit disorder Awareness, behavioral change and Bali Action Plan (2007) Bargaining games. See also Game Theory; Theory of Games; Ultimatum Games Batson, Daniel Bayes, Thomas Bayes’ Rule Bayesian updating Behavior acceptable awareness and collective Behavior (continued) decision making and descriptive models of individual learned managerial market motivating myopic neuroscience and rational social uncertainty/risk and Behavioral biases Behavioral data, linking(fig.)

Rage Inside the Machine: The Prejudice of Algorithms, and How to Stop the Internet Making Bigots of Us All by Robert Elliott Smith

"World Economic Forum" Davos, Ada Lovelace, adjacent possible, affirmative action, AI winter, Alfred Russel Wallace, algorithmic bias, algorithmic management, AlphaGo, Amazon Mechanical Turk, animal electricity, autonomous vehicles, behavioural economics, Black Swan, Brexit referendum, British Empire, Cambridge Analytica, cellular automata, Charles Babbage, citizen journalism, Claude Shannon: information theory, combinatorial explosion, Computing Machinery and Intelligence, corporate personhood, correlation coefficient, crowdsourcing, Daniel Kahneman / Amos Tversky, data science, deep learning, DeepMind, desegregation, discovery of DNA, disinformation, Douglas Hofstadter, Elon Musk, fake news, Fellow of the Royal Society, feminist movement, Filter Bubble, Flash crash, Geoffrey Hinton, Gerolamo Cardano, gig economy, Gödel, Escher, Bach, invention of the wheel, invisible hand, Jacquard loom, Jacques de Vaucanson, John Harrison: Longitude, John von Neumann, Kenneth Arrow, Linda problem, low skilled workers, Mark Zuckerberg, mass immigration, meta-analysis, mutually assured destruction, natural language processing, new economy, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, On the Economy of Machinery and Manufactures, p-value, pattern recognition, Paul Samuelson, performance metric, Pierre-Simon Laplace, post-truth, precariat, profit maximization, profit motive, Silicon Valley, social intelligence, statistical model, Stephen Hawking, stochastic process, Stuart Kauffman, telemarketer, The Bell Curve by Richard Herrnstein and Charles Murray, The Future of Employment, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, Thomas Malthus, traveling salesman, Turing machine, Turing test, twin studies, Vilfredo Pareto, Von Neumann architecture, warehouse robotics, women in the workforce, Yochai Benkler

In each case, reasoning from big data statistics (about your online profile, and those of many other people) are determining probabilities that are used to derive a desirable outcome. But most of these algorithms also involve an additional probability rule, which was furnished in 1761 by London Presbyterian minister Thomas Bayes. Little is known about Thomas Bayes other than he was a Fellow of the Royal Society and he wrote two papers on mathematics, one of which, Essay Towards Solving a Problem in the Doctrine of Chances (published after his death in 1761), laid out the final foundational rule of modern probability theory. Bayes’ rule follows trivially from the event-size-and-zoom-based arguments presented below, as shown in Figure 3.3.

Human Compatible: Artificial Intelligence and the Problem of Control by Stuart Russell

3D printing, Ada Lovelace, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Alfred Russel Wallace, algorithmic bias, AlphaGo, Andrew Wiles, artificial general intelligence, Asilomar, Asilomar Conference on Recombinant DNA, augmented reality, autonomous vehicles, basic income, behavioural economics, Bletchley Park, blockchain, Boston Dynamics, brain emulation, Cass Sunstein, Charles Babbage, Claude Shannon: information theory, complexity theory, computer vision, Computing Machinery and Intelligence, connected car, CRISPR, crowdsourcing, Daniel Kahneman / Amos Tversky, data science, deep learning, deepfake, DeepMind, delayed gratification, Demis Hassabis, Elon Musk, en.wikipedia.org, Erik Brynjolfsson, Ernest Rutherford, fake news, Flash crash, full employment, future of work, Garrett Hardin, Geoffrey Hinton, Gerolamo Cardano, Goodhart's law, Hans Moravec, ImageNet competition, Intergovernmental Panel on Climate Change (IPCC), Internet of things, invention of the wheel, job automation, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John Nash: game theory, John von Neumann, Kenneth Arrow, Kevin Kelly, Law of Accelerating Returns, luminiferous ether, machine readable, machine translation, Mark Zuckerberg, multi-armed bandit, Nash equilibrium, Nick Bostrom, Norbert Wiener, NP-complete, OpenAI, openstreetmap, P = NP, paperclip maximiser, Pareto efficiency, Paul Samuelson, Pierre-Simon Laplace, positional goods, probability theory / Blaise Pascal / Pierre de Fermat, profit maximization, RAND corporation, random walk, Ray Kurzweil, Recombinant DNA, recommendation engine, RFID, Richard Thaler, ride hailing / ride sharing, Robert Shiller, robotic process automation, Rodney Brooks, Second Machine Age, self-driving car, Shoshana Zuboff, Silicon Valley, smart cities, smart contracts, social intelligence, speech recognition, Stephen Hawking, Steven Pinker, superintelligent machines, surveillance capitalism, Thales of Miletus, The Future of Employment, The Theory of the Leisure Class by Thorstein Veblen, Thomas Bayes, Thorstein Veblen, Tragedy of the Commons, transport as a service, trolley problem, Turing machine, Turing test, universal basic income, uranium enrichment, vertical integration, Von Neumann architecture, Wall-E, warehouse robotics, Watson beat the top human players on Jeopardy!, web application, zero-sum game

Roughly speaking, Bayesian networks are the probabilistic cousins of propositional logic. There are also probabilistic cousins of first-order logic, including Bayesian logic58 and a wide variety of probabilistic programming languages. Bayesian networks and Bayesian logic are named after the Reverend Thomas Bayes, a British clergyman whose lasting contribution to modern thought—now known as Bayes’ theorem—was published in 1763, shortly after his death, by his friend Richard Price.59 In its modern form, as suggested by Laplace, the theorem describes in a very simple way how a prior probability—the initial degree of belief one has in a set of possible hypotheses—becomes a posterior probability as a result of observing some evidence.

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Courcier, 1814). 58. Bayesian logic described in a fairly nontechnical way: Stuart Russell, “Unifying logic and probability,” Communications of the ACM 58 (2015): 88–97. The paper draws heavily on the PhD thesis research of my former student Brian Milch. 59. The original source for Bayes’ theorem: Thomas Bayes and Richard Price, “An essay towards solving a problem in the doctrine of chances,” Philosophical Transactions of the Royal Society of London 53 (1763): 370–418. 60. Technically, Samuel’s program did not treat winning and losing as absolute rewards; by fixing the value of material to be positive; however, the program generally tended to work towards winning. 61.

Information: A Very Short Introduction by Luciano Floridi

agricultural Revolution, Albert Einstein, bioinformatics, Bletchley Park, carbon footprint, Claude Shannon: information theory, Computing Machinery and Intelligence, conceptual framework, digital divide, disinformation, double helix, Douglas Engelbart, Douglas Engelbart, George Akerlof, Gordon Gekko, Gregor Mendel, industrial robot, information asymmetry, intangible asset, Internet of things, invention of writing, John Nash: game theory, John von Neumann, Laplace demon, machine translation, moral hazard, Nash equilibrium, Nelson Mandela, Norbert Wiener, Pareto efficiency, phenotype, Pierre-Simon Laplace, prisoner's dilemma, RAND corporation, RFID, Thomas Bayes, Turing machine, Vilfredo Pareto

Jill has just identified a way of acquiring (learning) the missing piece of information that will help her to adopt the right strategy: if the chance that some emails in the quarantine folder might not be infected is very low, she will check it only occasionally. How could she obtain such a missing piece of information? The answer is by using a Bayesian approach. Thomas Bayes (1702-1761) was a Presbyterian minister and English mathematician whose investigations into probability, published posthumously, led to what is now known as Bayes' theorem and a new branch of applications of probability theory. The theorem calculates the posterior probability of an eventA given event B (that is, P(AIB) on the basis of the prior probability ofA (that is, P(A)).

The Great Mental Models: General Thinking Concepts by Shane Parrish

Albert Einstein, anti-fragile, Atul Gawande, Barry Marshall: ulcers, bitcoin, Black Swan, colonial rule, correlation coefficient, correlation does not imply causation, cuban missile crisis, Daniel Kahneman / Amos Tversky, dark matter, delayed gratification, feminist movement, Garrett Hardin, if you see hoof prints, think horses—not zebras, index fund, Isaac Newton, Jane Jacobs, John Bogle, Linda problem, mandelbrot fractal, Pepsi Challenge, Philippa Foot, Pierre-Simon Laplace, Ponzi scheme, Richard Feynman, statistical model, stem cell, The Death and Life of Great American Cities, the map is not the territory, the scientific method, Thomas Bayes, Torches of Freedom, Tragedy of the Commons, trolley problem

What is it and how can I use it to my advantage? There are three important aspects of probability that we need to explain so you can integrate them into your thinking to get into the ballpark and improve your chances of catching the ball: Bayesian thinking Fat-tailed curves Asymmetries Thomas Bayes and Bayesian thinking: Bayes was an English minister in the first half of the 18th century, whose most famous work, “An Essay Toward Solving a Problem in the Doctrine of Chances”, was brought to the attention of the Royal Society by his friend Richard Price in 1763—two years after his death. The essay concerned how we should adjust probabilities when we encounter new data, and provided the seeds for the great mathematician Pierre Simon Laplace to develop what we now call Bayes’s Theorem.

Statistics in a Nutshell by Sarah Boslaugh

Antoine Gombaud: Chevalier de Méré, Bayesian statistics, business climate, computer age, confounding variable, correlation coefficient, experimental subject, Florence Nightingale: pie chart, income per capita, iterative process, job satisfaction, labor-force participation, linear programming, longitudinal study, meta-analysis, p-value, pattern recognition, placebo effect, probability theory / Blaise Pascal / Pierre de Fermat, publication bias, purchasing power parity, randomized controlled trial, selection bias, six sigma, sparse data, statistical model, systematic bias, The Design of Experiments, the scientific method, Thomas Bayes, Two Sigma, Vilfredo Pareto

Another example of using Bayes’ theorem to calculate the probability of disease, given a positive test; note the lower rate of true positives, due to a lower rate of disease in the population In this example, less than one third of the positives are true positives. The Reverend Thomas Bayes Bayes’ theorem was developed by a British Nonconformist minister, the Reverend Thomas Bayes (1702–1761). Bayes studied logic and theology at the University of Edinburgh and earned his livelihood as a minister in Holborn and Tunbridge Wells, England. However, his fame today rests on his theory of probability, which was developed in his essay, published after his death by the Royal Society of London.

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Interval for a Proportion, Standard Error and Confidence Intervals about, Confidence Intervals–Confidence Intervals calculating for risk ratio, The Risk Ratio critiquing in articles, Standard Error and Confidence Intervals for independent samples (two-sample) t-test, Confidence Interval for the Independent Samples t-Test for one-sample t-test, Confidence Interval for the One-Sample t-Test–Confidence Interval for the One-Sample t-Test for proportions, Confidence Interval for a Proportion repeated measures (related samples) t-test, Confidence Interval for the Repeated Measures t-Test–Confidence Interval for the Repeated Measures t-Test confounding, Confounding, Stratified Analysis, and the Mantel-Haenszel Common Odds Ratio–Confounding, Stratified Analysis, and the Mantel-Haenszel Common Odds Ratio confounding variable, Glossary of Statistical Terms Conover, William, Practical Nonparametric Statistics, Nonparametric Statistics consistency measurements, Measures of Internal Consistency construct validity, Glossary of Statistical Terms Consumer Price Index (CPI), Index Numbers, Index Numbers content validity, Validity, Glossary of Statistical Terms contingency tables, The R×C Table–The R×C Table, The Risk Ratio R×C table, The R×C Table–The R×C Table two-by-two table, The Risk Ratio continuous data, Continuous and Discrete Data, Glossary of Statistical Terms definition of, Glossary of Statistical Terms vs. discrete data, Continuous and Discrete Data continuous variables, relationships between, Relationships Between Continuous Variables–Relationships Between Continuous Variables control charts and run charts, Run Charts and Control Charts control variables, Independent and Dependent Variables, Observational Studies, Glossary of Statistical Terms about, Independent and Dependent Variables definition of, Glossary of Statistical Terms in observational studies, Observational Studies controls, Identifying Treatments and Controls, Controls in experimental design, Identifying Treatments and Controls issues with, Controls convenience samples, Nonprobability Sampling Cook, Thomas D., Basic Vocabulary, Quasi-Experimental Studies, Quasi-Experimental Studies correlation statistics for categorical data, Binary Variables–Ordinal Variables correlations, The Pearson Correlation Coefficient, Association–Association, Scatterplots–Relationships Between Continuous Variables, Relationships Between Continuous Variables–Relationships Between Continuous Variables, The Pearson Correlation Coefficient–Testing Statistical Significance for the Pearson Correlation, Testing Statistical Significance for the Pearson Correlation–Testing Statistical Significance for the Pearson Correlation, The Coefficient of Determination, Methods for Building Regression Models about, The Pearson Correlation Coefficient associations, Association–Association coefficient of determination, The Coefficient of Determination correlation coefficient, The Pearson Correlation Coefficient–Testing Statistical 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Regression–Polynomial Regression cumulative frequency, Frequency Tables Cumulative Incidence (CI), Prevalence and Incidence CV (Coefficient of Variation), The Variance and Standard Deviation–The Variance and Standard Deviation D data, Statistics in the Age of Information, Basic Concepts of Measurement, Basic Concepts of Measurement–Proxy Measurement, The Rectangular Data File, String and Numeric Data–Missing Data, Gathering Experimental Data–Blocking and the Latin Square, Evaluating the Whole Article converting information into, Basic Concepts of Measurement critiquing in articles, Evaluating the Whole Article gathering experimental data, Gathering Experimental Data–Blocking and the Latin Square meaning of, Statistics in the Age of Information missing data, String and Numeric Data–Missing Data types of, Basic Concepts of Measurement–Proxy Measurement unit of analysis, The Rectangular Data File data management, Data Management–Data Management, An Approach, Not a Set of Recipes–An Approach, Not a Set of Recipes, The Chain of Command, Codebooks–Codebooks, Codebooks–The Rectangular Data File, Spreadsheets and Relational Databases–Spreadsheets and Relational Databases, Spreadsheets and Relational Databases, Inspecting a New Data File–Inspecting a New Data File, Inspecting a New Data File, Inspecting a New Data File, String and Numeric Data, String and Numeric Data–Missing Data about, Data Management–Data Management approach to, An Approach, Not a Set of Recipes–An Approach, Not a Set of Recipes codebooks, Codebooks–Codebooks data entry software, Spreadsheets and Relational Databases in projects, The Chain of Command inspecting new data file, Inspecting a New Data File–Inspecting a New Data File missing data, String and Numeric Data–Missing Data spreadsheets and relational databases for, Spreadsheets and Relational Databases–Spreadsheets and Relational Databases storing data electronically in rectangular data file, Codebooks–The Rectangular Data File string and numeric data, String and Numeric Data unique identifier in, Inspecting a New Data File variable names in transfer process to software, Inspecting a New Data File data mining vs. hypothesis testing, Specifying Response Variables data transformations, Data Transformations–Data Transformations data types, Basic Vocabulary databases, for data management, Spreadsheets and Relational Databases–Spreadsheets and Relational Databases decision analysis, Decision Analysis–Decision Trees decision trees, Decision Trees decision-making, Decision Analysis, Decision Analysis, Decision Analysis under certainty, Decision Analysis under risk, Decision Analysis under uncertainty, Decision Analysis degrees of freedom, Glossary of Statistical Terms Deming, W.

The Price of Tomorrow: Why Deflation Is the Key to an Abundant Future by Jeff Booth

3D printing, Abraham Maslow, activist fund / activist shareholder / activist investor, additive manufacturing, AI winter, Airbnb, Albert Einstein, AlphaGo, Amazon Web Services, artificial general intelligence, augmented reality, autonomous vehicles, basic income, bitcoin, blockchain, Bretton Woods, business intelligence, butterfly effect, Charles Babbage, Claude Shannon: information theory, clean water, cloud computing, cognitive bias, collapse of Lehman Brothers, Computing Machinery and Intelligence, corporate raider, creative destruction, crony capitalism, crowdsourcing, cryptocurrency, currency manipulation / currency intervention, dark matter, deep learning, DeepMind, deliberate practice, digital twin, distributed ledger, Donald Trump, Elon Musk, fiat currency, Filter Bubble, financial engineering, full employment, future of work, game design, gamification, general purpose technology, Geoffrey Hinton, Gordon Gekko, Great Leap Forward, Hyman Minsky, hype cycle, income inequality, inflation targeting, information asymmetry, invention of movable type, Isaac Newton, Jeff Bezos, John Maynard Keynes: Economic Possibilities for our Grandchildren, John von Neumann, Joseph Schumpeter, late fees, low interest rates, Lyft, Maslow's hierarchy, Milgram experiment, Minsky moment, Modern Monetary Theory, moral hazard, Nelson Mandela, Network effects, Nick Bostrom, oil shock, OpenAI, pattern recognition, Ponzi scheme, quantitative easing, race to the bottom, ride hailing / ride sharing, self-driving car, software as a service, technoutopianism, TED Talk, the long tail, the scientific method, Thomas Bayes, Turing test, Uber and Lyft, uber lyft, universal basic income, winner-take-all economy, X Prize, zero-sum game

Much work from behavioural science, machine learning, and psychology suggests that the answer is yes, our brains do act like Bayesian probability machines, constantly making new predictions based on changing information from our senses and assigning probabilities to the outcomes. What is a Bayesian probability machine? A computer that works on Bayes’s theorem, named after Thomas Bayes (1702–1761). Bayes’s theorem assesses the probability of an event based on prior information. My favourite example comes from Pedro Domingos’s book The Master Algorithm. In it, Domingos imagines a person waking up on a planet one afternoon at the beginning of time and seeing the sun go down and wondering if it will come back up.

Data Science for Business: What You Need to Know About Data Mining and Data-Analytic Thinking by Foster Provost, Tom Fawcett

Albert Einstein, Amazon Mechanical Turk, Apollo 13, big data - Walmart - Pop Tarts, bioinformatics, business process, call centre, chief data officer, Claude Shannon: information theory, computer vision, conceptual framework, correlation does not imply causation, crowdsourcing, data acquisition, data science, David Brooks, en.wikipedia.org, Erik Brynjolfsson, Gini coefficient, Helicobacter pylori, independent contractor, information retrieval, intangible asset, iterative process, Johann Wolfgang von Goethe, Louis Pasteur, Menlo Park, Nate Silver, Netflix Prize, new economy, p-value, pattern recognition, placebo effect, price discrimination, recommendation engine, Ronald Coase, selection bias, Silicon Valley, Skype, SoftBank, speech recognition, Steve Jobs, supply-chain management, systems thinking, Teledyne, text mining, the long tail, The Signal and the Noise by Nate Silver, Thomas Bayes, transaction costs, WikiLeaks

We could just as well have written: This means: And so: If we divide both sides by p(A) we get: Now, let’s consider B to be some hypothesis that we are interested in assessing the likelihood of, and A to be some evidence that we have observed. Renaming with H for hypothesis and E for evidence, we get: This is the famous Bayes’ Rule, named after the Reverend Thomas Bayes who derived a special case of the rule back in the 18th century. Bayes’ Rule says that we can compute the probability of our hypothesis H given some evidence E by instead looking at the probability of the evidence given the hypothesis, as well as the unconditional probabilities of the hypothesis and the evidence.

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Data Reduction, Latent Information, and Movie Recommendation benefit improvement, calculating, Costs and benefits benefits and underlying profit calculation, ROC Graphs and Curves data-driven decision-making, Data Science, Engineering, and Data-Driven Decision Making estimating, Costs and benefits in budgeting, Ranking Instead of Classifying nearest-neighbor methods, Computational efficiency bi-grams, N-gram Sequences bias errors, ensemble methods and, Bias, Variance, and Ensemble Methods–Bias, Variance, and Ensemble Methods Big Data data science and, Data Processing and “Big Data”–Data Processing and “Big Data” evolution of, From Big Data 1.0 to Big Data 2.0–From Big Data 1.0 to Big Data 2.0 on Amazon and Google, Thinking Data-Analytically, Redux big data technologies, Data Processing and “Big Data” state of, From Big Data 1.0 to Big Data 2.0 utilizing, Data Processing and “Big Data” Big Red proposal example, Example Data Mining Proposal–Flaws in the Big Red Proposal Bing, Why Text Is Important, Representation Black-Sholes model, Models, Induction, and Prediction blog postings, Why Text Is Important blog posts, Example: Targeting Online Consumers With Advertisements Borders (book retailer), Achieving Competitive Advantage with Data Science breast cancer example, Example: Logistic Regression versus Tree Induction–Example: Logistic Regression versus Tree Induction Brooks, David, What Data Can’t Do: Humans in the Loop, Revisited browser cookies, Example: Targeting Online Consumers With Advertisements Brubeck, Dave, Example: Jazz Musicians Bruichladdich single malt scotch, Understanding the Results of Clustering Brynjolfsson, Erik, Data Science, Engineering, and Data-Driven Decision Making, Data Processing and “Big Data” budget, Ranking Instead of Classifying budget constraints, Profit Curves building modeling labs, From Holdout Evaluation to Cross-Validation building models, Data Mining and Its Results, Business Understanding, From Holdout Evaluation to Cross-Validation Bunnahabhain single malt whiskey, Example: Whiskey Analytics, Hierarchical Clustering business news stories example, Example: Clustering Business News Stories–The news story clusters business problems changing definition of, to fit available data, Changing the Way We Think about Solutions to Business Problems–Changing the Way We Think about Solutions to Business Problems data exploration vs., Stepping Back: Solving a Business Problem Versus Data Exploration–Stepping Back: Solving a Business Problem Versus Data Exploration engineering problems vs., Other Data Science Tasks and Techniques evaluating in a proposal, Be Ready to Evaluate Proposals for Data Science Projects expected value framework, structuring with, The Expected Value Framework: Structuring a More Complicated Business Problem–The Expected Value Framework: Structuring a More Complicated Business Problem exploratory data mining vs., The Fundamental Concepts of Data Science unique context of, What Data Can’t Do: Humans in the Loop, Revisited using expected values to provide framework for, The Expected Value Framework: Decomposing the Business Problem and Recomposing the Solution Pieces–The Expected Value Framework: Decomposing the Business Problem and Recomposing the Solution Pieces business strategy, Data Science and Business Strategy–A Firm’s Data Science Maturity accepting creative ideas, Be Ready to Accept Creative Ideas from Any Source case studies, examining, Examine Data Science Case Studies competitive advantages, Achieving Competitive Advantage with Data Science–Achieving Competitive Advantage with Data Science, Sustaining Competitive Advantage with Data Science–Superior Data Science Management data scientists, evaluating, Superior Data Scientists–Superior Data Scientists evaluating proposals, Be Ready to Evaluate Proposals for Data Science Projects–Flaws in the Big Red Proposal historical advantages and, Formidable Historical Advantage intangible collateral assets and, Unique 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In Pursuit of the Perfect Portfolio: The Stories, Voices, and Key Insights of the Pioneers Who Shaped the Way We Invest by Andrew W. Lo, Stephen R. Foerster

Alan Greenspan, Albert Einstein, AOL-Time Warner, asset allocation, backtesting, behavioural economics, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, Charles Babbage, Charles Lindbergh, compound rate of return, corporate governance, COVID-19, credit crunch, currency risk, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, Edward Glaeser, equity premium, equity risk premium, estate planning, Eugene Fama: efficient market hypothesis, fake news, family office, fear index, fiat currency, financial engineering, financial innovation, financial intermediation, fixed income, hiring and firing, Hyman Minsky, implied volatility, index fund, interest rate swap, Internet Archive, invention of the wheel, Isaac Newton, Jim Simons, John Bogle, John Meriwether, John von Neumann, joint-stock company, junk bonds, Kenneth Arrow, linear programming, Long Term Capital Management, loss aversion, Louis Bachelier, low interest rates, managed futures, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, money market fund, money: store of value / unit of account / medium of exchange, Myron Scholes, new economy, New Journalism, Own Your Own Home, passive investing, Paul Samuelson, Performance of Mutual Funds in the Period, prediction markets, price stability, profit maximization, quantitative trading / quantitative finance, RAND corporation, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Solow, Ronald Reagan, Savings and loan crisis, selection bias, seminal paper, shareholder value, Sharpe ratio, short selling, South Sea Bubble, stochastic process, stocks for the long run, survivorship bias, tail risk, Thales and the olive presses, Thales of Miletus, The Myth of the Rational Market, The Wisdom of Crowds, Thomas Bayes, time value of money, transaction costs, transfer pricing, tulip mania, Vanguard fund, yield curve, zero-coupon bond, zero-sum game

in which he made the distinction between the concept of market efficiency—processing information correctly—and the statement that the market portfolio of all stocks is a mean-variance efficient portfolio (we’ll return to the topic of market efficiency in chapter 4).99 Bill Sharpe’s capital asset pricing model, discussed in chapter 3, makes an important assumption that all investors can borrow or lend without constraint at the same rate of interest. Without that key assumption, Markowitz argues, there is nothing special about the market portfolio. To further describe his approach to the Perfect Portfolio, Markowitz took the perspective originally attributed to Thomas Bayes, the mathematician who created a new branch of probability theory that relied on the notion that when individuals receive new information, they update their beliefs about the probability of events they expect to take place. “Assume we are Bayesians. If we don’t have the same prior [beliefs], we shouldn’t have the same portfolios.

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“Efficient Portfolios, Sparse Matrices, and Entities: A Retrospective.” Operations Research 50, no. 1: 154–60. ________. 2005. “Market Efficiency: A Theoretical Distinction and So What?” Financial Analysts Journal 61, no. 5: 17–30. ________. 2006. “De Finetti Scoops Markowitz.” Journal of Investment Management 4: 5–18. ________. 2010. “God, Ants and Thomas Bayes.” American Economist 55, no. 2: 5–9. ________. 2016. Risk-Return Analysis, Vol. 2, The Theory and Practice of Rational Investing. New York: McGraw-Hill. ________. 2020. Risk-Return Analysis, Vol. 3, The Theory and Practice of Rational Investing. New York: McGraw-Hill. Markowitz, Harry M., and Kenneth Blay. 2014.

Content: Selected Essays on Technology, Creativity, Copyright, and the Future of the Future by Cory Doctorow

AltaVista, AOL-Time Warner, book scanning, Brewster Kahle, Burning Man, cognitive load, drop ship, en.wikipedia.org, general purpose technology, informal economy, information retrieval, Internet Archive, invention of movable type, Jeff Bezos, John Gilmore, John Perry Barlow, Law of Accelerating Returns, machine readable, Metcalfe's law, mirror neurons, Mitch Kapor, moral panic, mutually assured destruction, Neal Stephenson, new economy, optical character recognition, PalmPilot, patent troll, pattern recognition, peer-to-peer, Ponzi scheme, post scarcity, QWERTY keyboard, Ray Kurzweil, RFID, Sand Hill Road, Skype, slashdot, Snow Crash, social software, speech recognition, Steve Jobs, the long tail, Thomas Bayes, Turing test, Vernor Vinge, Wayback Machine

It’s a handsome old boneyard, a former plague pit (“Bone hill” — as in, there are so many bones under there that the ground is actually kind of humped up into a hill). There are plenty of luminaries buried there — John “Pilgrim’s Progress” Bunyan, William Blake, Daniel Defoe, and assorted Cromwells. But my favorite tomb is that of Thomas Bayes, the 18th-century statistician for whom Bayesian filtering is named. Bayesian filtering is plenty useful. Here’s a simple example of how you might use a Bayesian filter. First, get a giant load of non-spam emails and feed them into a Bayesian program that counts how many times each word in their vocabulary appears, producing a statistical breakdown of the word-frequency in good emails.

Demystifying Smart Cities by Anders Lisdorf

3D printing, artificial general intelligence, autonomous vehicles, backpropagation, behavioural economics, Big Tech, bike sharing, bitcoin, business intelligence, business logic, business process, chief data officer, circular economy, clean tech, clean water, cloud computing, computer vision, Computing Machinery and Intelligence, congestion pricing, continuous integration, crowdsourcing, data is the new oil, data science, deep learning, digital rights, digital twin, distributed ledger, don't be evil, Elon Musk, en.wikipedia.org, facts on the ground, Google Glasses, hydroponic farming, income inequality, information security, Infrastructure as a Service, Internet of things, Large Hadron Collider, Masdar, microservices, Minecraft, OSI model, platform as a service, pneumatic tube, ransomware, RFID, ride hailing / ride sharing, risk tolerance, Salesforce, self-driving car, smart cities, smart meter, software as a service, speech recognition, Stephen Hawking, Steve Jobs, Steve Wozniak, Stuxnet, Thomas Bayes, Turing test, urban sprawl, zero-sum game

Use cases for cities would be in computer vision where images could be converted into counts of pedestrians, cars, and bicycles or for allowing speech interaction with city services. The resident could speak, and the input converted into text that could then be processed as questions and answers. Naïve Bayes – Based on Bayes’ theorem, the naïve Bayes algorithm aims to make probabilistic classification based on prior knowledge. Thomas Bayes was an Eighteenth-century English minister and philosopher who first proposed to use conditional probability. The basic assumption is that we can use prior knowledge to determine probabilities. If we know that smoking is an important factor in the probability of developing respiratory illnesses, it can be used to give us a probability of a given person developing a respiratory illness based on his or her smoking habits.

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures by Frank J. Fabozzi

algorithmic trading, Benoit Mandelbrot, Black Monday: stock market crash in 1987, capital asset pricing model, collateralized debt obligation, correlation coefficient, distributed generation, diversified portfolio, financial engineering, fixed income, global macro, index fund, junk bonds, Louis Bachelier, Myron Scholes, p-value, power law, quantitative trading / quantitative finance, random walk, risk free rate, risk-adjusted returns, short selling, stochastic volatility, subprime mortgage crisis, Thomas Bayes, transaction costs, value at risk

The Law of Total Probability for More than Two Events The expression for the Law of Total Probability in equation (15.6) can easily be generalized to the case of K events: The only “catch” is that we need to take care that the events B1, B2, …, BK exhaust the sample space (their probabilities sum up to 1) and are mutually exclusive. (In the two-event case, B and Bc clearly fulfil these requirements.) BAYES’ RULE Bayes’ rule, named after the eighteenth-century British mathematician Thomas Bayes, provides a method for expressing an unknown conditional probability P(B|A) with the help of the known conditional probability P(A|B). Bayes’ rule, for events A and B, is given by the following expression Another formulation of Bayes’ rule is by using the Law of Total Probability in the denominator in place of P(A).

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See also Negative autocorrelation; Positive autocorrelation detection presence, modeling Autoregressive conditional heteroskedasticity (ARCH) model generalization Autoregressive moving average (ARMA) models Autoregressive of order one Autoregressive process (AR) of order p Axiomatic system Bar chart usage Bayes, Thomas Bayes’ formula Bayes’ rule application Bell-shaped curve, real-life distribution Bell-shaped density Bell-shaped yield Benchmark, derivation Berkshire Hathway pie charts, comparison revenues, third quarter (pie chart) third quarter reports third quarter revenues bar charts pie chart Bermuda call option Bernoulli distributed random variable, mean/variance Bernoulli distribution generalization p parameter, estimation random variables, relationship Bernoulli population, sample mean (histogram) Bernoulli random variables distribution Bernoulli samples, examination Bernoulli trials, link Bessel function of the third kind defining Best linear unbiased estimator (BLUE) Beta distribution distribution function Beta factor Beta function Bias.

Programming Computer Vision with Python by Jan Erik Solem

augmented reality, computer vision, database schema, en.wikipedia.org, optical character recognition, pattern recognition, text mining, Thomas Bayes, web application

If you want to dive deeper into classifiers and machine learning algorithms, take a look at the scikit.learn package (http://scikit-learn.org/) and try some of the algorithms on the data in this chapter. * * * [21] Another option is to only keep a selected subset of the training set. This can, however, impact accuracy. [22] Another common name is Histogram of Oriented Gradients (HOG). [23] After Thomas Bayes, an 18th-century English mathematician and minister. [24] See http://en.wikipedia.org/wiki/Sudoku for more details if you are unfamiliar with the concept. [25] Images courtesy of Martin Byröd [4], http://www.maths.lth.se/matematiklth/personal/byrod/, collected and cropped from photos of actual Sudokus.

Everydata: The Misinformation Hidden in the Little Data You Consume Every Day by John H. Johnson

Affordable Care Act / Obamacare, autism spectrum disorder, Black Swan, business intelligence, Carmen Reinhart, cognitive bias, correlation does not imply causation, Daniel Kahneman / Amos Tversky, data science, Donald Trump, en.wikipedia.org, Kenneth Rogoff, labor-force participation, lake wobegon effect, Long Term Capital Management, Mercator projection, Mercator projection distort size, especially Greenland and Africa, meta-analysis, Nate Silver, obamacare, p-value, PageRank, pattern recognition, publication bias, QR code, randomized controlled trial, risk-adjusted returns, Ronald Reagan, selection bias, statistical model, The Signal and the Noise by Nate Silver, Thomas Bayes, Tim Cook: Apple, wikimedia commons, Yogi Berra

Ellen Davis, “Committing the ‘Gambler’s Fallacy’ May Be in the Cards, New Research Shows,” Texas A&M Health Science Center website, March 9, 2015, http://news.tamhsc.edu/?post=committing-the-gamblers-fallacy-may-be-in-the-cards-new-research-shows. Thanks to Ron Friedman for the find. 27. There’s another way of looking at this, known as Bayesian probability (after the eighteenth-century English mathematician Thomas Bayes). With Bayesian probability, you use the data gathered to update your initial beliefs after the fact. It’s the opposite of the way in which the gambler’s fallacy works. As one of John’s colleagues pointed out, it’s the difference between knowing that a coin is fair and learning about the coin.

The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age by Paul J. Nahin

air gap, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, Charles Babbage, Claude Shannon: information theory, Computing Machinery and Intelligence, conceptual framework, Edward Thorp, Fellow of the Royal Society, finite state, four colour theorem, Georg Cantor, Grace Hopper, Isaac Newton, John von Neumann, knapsack problem, New Journalism, Pierre-Simon Laplace, reversible computing, Richard Feynman, Schrödinger's Cat, Steve Jobs, Steve Wozniak, thinkpad, Thomas Bayes, Turing machine, Turing test, V2 rocket

Boole argued that this is not so, using the ideas of the previous section, and showed that P( | X) is given by a considerably more involved expression than simply “p.” What Boole did was not really original, as conditional probability had been studied a century before by the English philosopher and minister Thomas Bayes (1701–1761), whose work was published posthumously in 1764 in the Philosophical Transactions of the Royal Society of London, where it was then promptly forgotten for twenty years until the great French mathematician Pierre-Simon Laplace (1749–1827) endorsed Bayes’s results. What Boole did, then, with the following analysis, was remind his readers what the Reverend Bayes had done a hundred years before.

The Crash Detectives: Investigating the World's Most Mysterious Air Disasters by Christine Negroni

Air France Flight 447, Airbus A320, Boeing 747, Captain Sullenberger Hudson, Charles Lindbergh, Checklist Manifesto, computer age, crew resource management, crowdsourcing, flag carrier, low cost airline, Neil Armstrong, Richard Feynman, South China Sea, Tenerife airport disaster, Thomas Bayes, US Airways Flight 1549

Some of the credit for finally finding the submerged airliner goes to Metron Scientific Solutions, a company staffed with pencil-wielding mathematicians who used probability, logic, and numbers to conclude that the likely resting place of the plane was a narrow slice of ocean that had already been checked. “A lack of success tells you about where it is not, and that contributes to knowledge,” said Larry Stone, chief scientist at Metron. Talk about having a positive point of view. The Metron method is based on Bayesian probability, the theory of eighteenth-century statistician and philosopher Thomas Bayes, whose first published work, Divine Benevolence, was equally optimistic because it attempted to prove that God wants us to be happy. Using Bayesian logic to look for missing airplanes, as interpreted by Metron, involves taking all kinds of input about the missing thing (even conflicting input) and assigning levels of certainty or uncertainty to each.

Hello World: Being Human in the Age of Algorithms by Hannah Fry

23andMe, 3D printing, Air France Flight 447, Airbnb, airport security, algorithmic bias, algorithmic management, augmented reality, autonomous vehicles, backpropagation, Brixton riot, Cambridge Analytica, chief data officer, computer vision, crowdsourcing, DARPA: Urban Challenge, data science, deep learning, DeepMind, Douglas Hofstadter, driverless car, Elon Musk, fake news, Firefox, Geoffrey Hinton, Google Chrome, Gödel, Escher, Bach, Ignaz Semmelweis: hand washing, John Markoff, Mark Zuckerberg, meta-analysis, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, pattern recognition, Peter Thiel, RAND corporation, ransomware, recommendation engine, ride hailing / ride sharing, selection bias, self-driving car, Shai Danziger, Silicon Valley, Silicon Valley startup, Snapchat, sparse data, speech recognition, Stanislav Petrov, statistical model, Stephen Hawking, Steven Levy, systematic bias, TED Talk, Tesla Model S, The Wisdom of Crowds, Thomas Bayes, trolley problem, Watson beat the top human players on Jeopardy!, web of trust, William Langewiesche, you are the product

But where the Bayesian way of thinking really comes into its own is when you’re trying to consider more than one hypothesis simultaneously – for example, in attempting to diagnose what’s wrong with a patient on the basis of their symptoms,* or finding the position of a driverless car on the basis of sensor readings. In theory, any disease, any point on the map, could represent the underlying truth. All you need to do is weigh up the evidence to decide which is most likely to be right. And on that point, finding the location of a driverless car turns out to be rather similar to a problem that puzzled Thomas Bayes, the British Presbyterian minister and talented mathematician after whom the theorem is named. Back in the mid-1700s, he wrote an essay which included details of a game he’d devised to explain the problem. It went something a little like this:32 Imagine you’re sitting with your back to a square table.

On Intelligence by Jeff Hawkins, Sandra Blakeslee

airport security, Albert Einstein, backpropagation, computer age, Computing Machinery and Intelligence, conceptual framework, Jeff Hawkins, Johannes Kepler, Necker cube, PalmPilot, pattern recognition, Paul Erdős, Ray Kurzweil, Silicon Valley, Silicon Valley startup, speech recognition, superintelligent machines, the scientific method, Thomas Bayes, Turing machine, Turing test

Scientists such as David Mumford at Brown University, Rajesh Rao at the University of Washington, Stephen Grossberg at Boston University, and many more have written and theorized about the role of feedback and prediction in various ways. There is an entire subfield of mathematics devoted to Bayesian networks. Named after Thomas Bayes, an English minister born in 1702 who was a pioneer in statistics, Bayesian networks use probability theory to make predictions. What has been lacking is putting these disparate bits and pieces into a coherent theoretical framework. This, I argue, has not been done before, and it is the goal of this book

Beyond Weird by Philip Ball

Albert Einstein, Bayesian statistics, cosmic microwave background, dark matter, dark pattern, dematerialisation, Ernest Rutherford, experimental subject, Higgs boson, Isaac Newton, John von Neumann, Kickstarter, Large Hadron Collider, Murray Gell-Mann, quantum cryptography, quantum entanglement, Richard Feynman, Schrödinger's Cat, Stephen Hawking, theory of mind, Thomas Bayes

Those beliefs do not become realized as facts until they impinge on the consciousness of the observer – and so the facts are specific to every observer (although different observers can find themselves agreeing on the same facts). This notion takes its cue from standard Bayesian probability theory, introduced in the eighteenth century by the English mathematician and clergyman Thomas Bayes. In Bayesian statistics, probabilities are not defined with reference to some objective state of affairs in the world, but instead quantify personal degrees of belief of what might happen – which we update as we acquire new information. The QBist view, however, says something much more profound than simply that different people know different things.

AIQ: How People and Machines Are Smarter Together by Nick Polson, James Scott

Abraham Wald, Air France Flight 447, Albert Einstein, algorithmic bias, Amazon Web Services, Atul Gawande, autonomous vehicles, availability heuristic, basic income, Bayesian statistics, Big Tech, Black Lives Matter, Bletchley Park, business cycle, Cepheid variable, Checklist Manifesto, cloud computing, combinatorial explosion, computer age, computer vision, Daniel Kahneman / Amos Tversky, data science, deep learning, DeepMind, Donald Trump, Douglas Hofstadter, Edward Charles Pickering, Elon Musk, epigenetics, fake news, Flash crash, Grace Hopper, Gödel, Escher, Bach, Hans Moravec, Harvard Computers: women astronomers, Higgs boson, index fund, information security, Isaac Newton, John von Neumann, late fees, low earth orbit, Lyft, machine translation, Magellanic Cloud, mass incarceration, Moneyball by Michael Lewis explains big data, Moravec's paradox, more computing power than Apollo, natural language processing, Netflix Prize, North Sea oil, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, p-value, pattern recognition, Pierre-Simon Laplace, ransomware, recommendation engine, Ronald Reagan, Salesforce, self-driving car, sentiment analysis, side project, Silicon Valley, Skype, smart cities, speech recognition, statistical model, survivorship bias, systems thinking, the scientific method, Thomas Bayes, Uber for X, uber lyft, universal basic income, Watson beat the top human players on Jeopardy!, young professional

Bayes’s Rule, from Reverend to Robot Here’s the key mantra we must take away from the story of the Scorpion: all probabilities are really conditional probabilities. In other words, all probabilities are contingent upon what we know. When our knowledge changes, our probabilities must change, too—and Bayes’s rule tells us how to change them. Bayes’s rule was discovered by an obscure English clergyman named Thomas Bayes. Born in 1701 to a Presbyterian family in London, Bayes showed an early talent for mathematics, but he came of age at a time when religious dissenters were barred from universities in England. Denied the chance to study math at Oxford or Cambridge, he ended up studying theology at the University of Edinburgh instead.

Our Final Invention: Artificial Intelligence and the End of the Human Era by James Barrat

AI winter, air gap, AltaVista, Amazon Web Services, artificial general intelligence, Asilomar, Automated Insights, Bayesian statistics, Bernie Madoff, Bill Joy: nanobots, Bletchley Park, brain emulation, California energy crisis, cellular automata, Chuck Templeton: OpenTable:, cloud computing, cognitive bias, commoditize, computer vision, Computing Machinery and Intelligence, cuban missile crisis, Daniel Kahneman / Amos Tversky, Danny Hillis, data acquisition, don't be evil, drone strike, dual-use technology, Extropian, finite state, Flash crash, friendly AI, friendly fire, Google Glasses, Google X / Alphabet X, Hacker News, Hans Moravec, Isaac Newton, Jaron Lanier, Jeff Hawkins, John Markoff, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, Loebner Prize, lone genius, machine translation, mutually assured destruction, natural language processing, Neil Armstrong, Nicholas Carr, Nick Bostrom, optical character recognition, PageRank, PalmPilot, paperclip maximiser, pattern recognition, Peter Thiel, precautionary principle, prisoner's dilemma, Ray Kurzweil, Recombinant DNA, Rodney Brooks, rolling blackouts, Search for Extraterrestrial Intelligence, self-driving car, semantic web, Silicon Valley, Singularitarianism, Skype, smart grid, speech recognition, statistical model, stealth mode startup, stem cell, Stephen Hawking, Steve Jobs, Steve Jurvetson, Steve Wozniak, strong AI, Stuxnet, subprime mortgage crisis, superintelligent machines, technological singularity, The Coming Technological Singularity, Thomas Bayes, traveling salesman, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, zero day

He was not in his office but at home, perhaps calculating the probability of God’s existence. According to Dr. Holtzman, sometime before he died, Good updated that probability from zero to point one. He did this because as a statistician, he was a long-term Bayesian. Named for the eighteenth-century mathematician and minister Thomas Bayes, Bayesian statistics’ main idea is that in calculating the probability of some statement, you can start with a personal belief. Then you update that belief as new evidence comes in that supports your statement or doesn’t. If Good’s original disbelief in God had remained 100 percent, no amount of data, not even God’s appearance, could change his mind.

Know Thyself by Stephen M Fleming

Abraham Wald, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, AlphaGo, autism spectrum disorder, autonomous vehicles, availability heuristic, backpropagation, citation needed, computer vision, confounding variable, data science, deep learning, DeepMind, Demis Hassabis, Douglas Hofstadter, Dunning–Kruger effect, Elon Musk, Estimating the Reproducibility of Psychological Science, fake news, global pandemic, higher-order functions, index card, Jeff Bezos, l'esprit de l'escalier, Lao Tzu, lifelogging, longitudinal study, meta-analysis, mutually assured destruction, Network effects, patient HM, Pierre-Simon Laplace, power law, prediction markets, QWERTY keyboard, recommendation engine, replication crisis, self-driving car, side project, Skype, Stanislav Petrov, statistical model, theory of mind, Thomas Bayes, traumatic brain injury

Jonathan Steele, “Stanislav Petrov Obituary,” The Guardian, October 11, 2017, www.theguardian.com/world/2017/oct/11/stanislav-petrov-obituary. 2. Green and Swets (1966). 3. The seeds of Bayes’s rule were first identified by the eleventh-century Arabic mathematician Ibn al-Haytham, developed by English clergyman and mathematician Thomas Bayes in 1763, and applied to a range of scientific problems by the eighteenth-century French mathematician Pierre-Simon Laplace. See McGrayne (2012). 4. Felleman and Van Essen (1991); Zeki and Bartels (1998). 5. Clark (2013); Clark (2016); Craik (1963); Friston (2010); Helmholtz (1856); Gregory (1970); Hohwy (2013). 6.

How Medicine Works and When It Doesn't: Learning Who to Trust to Get and Stay Healthy by F. Perry Wilson

Affordable Care Act / Obamacare, barriers to entry, Barry Marshall: ulcers, cognitive bias, Comet Ping Pong, confounding variable, coronavirus, correlation does not imply causation, COVID-19, data science, Donald Trump, fake news, Helicobacter pylori, Ignaz Semmelweis: hand washing, Louis Pasteur, medical malpractice, meta-analysis, multilevel marketing, opioid epidemic / opioid crisis, p-value, personalized medicine, profit motive, randomized controlled trial, risk tolerance, selection bias, statistical model, stem cell, sugar pill, the scientific method, Thomas Bayes

Each time that link was demonstrated, my belief in my wife’s hypothesis strengthened, and my belief in my own hypothesis weakened. Eventually, the weight of evidence was too much to bear, and I conceded she was probably right. These kids are crazy, but they are extra-crazy with chocolate in their systems. Allowing the slow, methodical updating of your prior beliefs based on new data is a form of Bayesian reasoning. Thomas Bayes was an eighteenth-century English minister and statistician whose eponymous theorem demonstrated, mathematically, how new information can be used to update prior knowledge. It is a centerpiece of statistics to this day, and the bane of many undergraduate stats majors. But Bayesian reasoning is quite similar to how the human mind works, at least when we are not unreasonably tethered to conclusions we want or need to be true.

The Singularity Is Near: When Humans Transcend Biology by Ray Kurzweil

additive manufacturing, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, backpropagation, Benoit Mandelbrot, Bill Joy: nanobots, bioinformatics, brain emulation, Brewster Kahle, Brownian motion, business cycle, business intelligence, c2.com, call centre, carbon-based life, cellular automata, Charles Babbage, Claude Shannon: information theory, complexity theory, conceptual framework, Conway's Game of Life, coronavirus, cosmological constant, cosmological principle, cuban missile crisis, data acquisition, Dava Sobel, David Brooks, Dean Kamen, digital divide, disintermediation, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, factory automation, friendly AI, functional programming, George Gilder, Gödel, Escher, Bach, Hans Moravec, hype cycle, informal economy, information retrieval, information security, invention of the telephone, invention of the telescope, invention of writing, iterative process, Jaron Lanier, Jeff Bezos, job automation, job satisfaction, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, lifelogging, linked data, Loebner Prize, Louis Pasteur, mandelbrot fractal, Marshall McLuhan, Mikhail Gorbachev, Mitch Kapor, mouse model, Murray Gell-Mann, mutually assured destruction, natural language processing, Network effects, new economy, Nick Bostrom, Norbert Wiener, oil shale / tar sands, optical character recognition, PalmPilot, pattern recognition, phenotype, power law, precautionary principle, premature optimization, punch-card reader, quantum cryptography, quantum entanglement, radical life extension, randomized controlled trial, Ray Kurzweil, remote working, reversible computing, Richard Feynman, Robert Metcalfe, Rodney Brooks, scientific worldview, Search for Extraterrestrial Intelligence, selection bias, semantic web, seminal paper, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, Stuart Kauffman, superintelligent machines, technological singularity, Ted Kaczynski, telepresence, The Coming Technological Singularity, Thomas Bayes, transaction costs, Turing machine, Turing test, two and twenty, Vernor Vinge, Y2K, Yogi Berra

He plans to develop a system incorporating all human ideas.167 One application would be to inform policy makers of which ideas are held by which community. Bayesian Nets. Over the last decade a technique called Bayesian logic has created a robust mathematical foundation for combining thousands or even millions of such probabilistic rules in what are called "belief networks" or Bayesian nets. Originally devised by English mathematician Thomas Bayes and published posthumously in 1763, the approach is intended to determine the likelihood of future events based on similar occurrences in the past.168 Many expert systems based on Bayesian techniques gather data from experience in an ongoing fashion, thereby continually learning and improving their decision making.

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Kristen Philipkoski, "Now Here's a Really Big Idea," Wired News, November 25, 2002, http://www.wired.com/news/technology/0,1282,56374,00.html, reporting on Darryl Macer, "The Next Challenge Is to Map the Human Mind," Nature 420 (November 14, 2002): 121; see also a description of the project at http://www.biol.tsukuba.ac.jp/~macer/index.html. 168. Thomas Bayes, "An Essay Towards Solving a Problem in the Doctrine of Chances," published in 1763, two years after his death in 1761. 169. SpamBayes spam filter, http://spambayes.sourceforge.net. 170. Lawrence R. Rabiner, "A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition," Proceedings of the IEEE 77 (1989): 257–86.

The Most Human Human: What Talking With Computers Teaches Us About What It Means to Be Alive by Brian Christian

"Friedman doctrine" OR "shareholder theory", 4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Bertrand Russell: In Praise of Idleness, Blue Ocean Strategy, carbon footprint, cellular automata, Charles Babbage, Claude Shannon: information theory, cognitive dissonance, commoditize, complexity theory, Computing Machinery and Intelligence, crowdsourcing, David Heinemeier Hansson, Donald Trump, Douglas Hofstadter, George Akerlof, Gödel, Escher, Bach, high net worth, Isaac Newton, Jacques de Vaucanson, Jaron Lanier, job automation, Kaizen: continuous improvement, Ken Thompson, l'esprit de l'escalier, language acquisition, Loebner Prize, machine translation, Menlo Park, operational security, Ray Kurzweil, RFID, Richard Feynman, Ronald Reagan, SimCity, Skype, Social Responsibility of Business Is to Increase Its Profits, starchitect, statistical model, Stephen Hawking, Steve Jobs, Steven Pinker, Thales of Miletus, theory of mind, Thomas Bayes, Turing machine, Turing test, Von Neumann architecture, Watson beat the top human players on Jeopardy!, zero-sum game

I walk out of the Brighton Centre, to the bracing sea air for a minute, and into a small, locally owned shoe store looking for a gift to bring back home to my girlfriend; the shopkeeper notices my accent; I tell her I’m from Seattle; she is a grunge fan; I comment on the music playing in the store; she says it’s Florence + the Machine; I tell her I like it and that she would probably like Feist … I walk into a tea and scone store called the Mock Turtle and order the British equivalent of coffee and a donut, except it comes with thirteen pieces of silverware and nine pieces of flatware; I am so in England, I think; an old man, probably in his eighties, is shakily eating a pastry the likes of which I’ve never seen; I ask him what it is; “coffee meringue,” he says and remarks on my accent; an hour later he is telling me about World War II, the exponentially increasing racial diversity of Britain, that House of Cards is a pretty accurate depiction of British politics, minus the murders, but that really I should watch Spooks; do you get Spooks on cable, he is asking me … I meet my old boss for dinner; and after a couple years of being his research assistant and occasionally co-author, and after a brief thought of becoming one of his Ph.D. students, after a year of our paths not really crossing, we negotiate whether our formerly collegial and hierarchical relationship, now that its context is removed, simply dries up or flourishes into a domain-general friendship; we are ordering appetizers and saying something about Wikipedia, something about Thomas Bayes, something about vegetarian dining … Laurels are of no use. If you de-anonymized yourself in the past, great. But that was that. And now, you begin again. 1. These logs would, three years later, be put on the IBM website, albeit in incomplete form and with so little fanfare that Kasparov himself wouldn’t find out about them until 2005.

Superforecasting: The Art and Science of Prediction by Philip Tetlock, Dan Gardner

Affordable Care Act / Obamacare, Any sufficiently advanced technology is indistinguishable from magic, availability heuristic, behavioural economics, Black Swan, butterfly effect, buy and hold, cloud computing, cognitive load, cuban missile crisis, Daniel Kahneman / Amos Tversky, data science, desegregation, drone strike, Edward Lorenz: Chaos theory, forward guidance, Freestyle chess, fundamental attribution error, germ theory of disease, hindsight bias, How many piano tuners are there in Chicago?, index fund, Jane Jacobs, Jeff Bezos, Kenneth Arrow, Laplace demon, longitudinal study, Mikhail Gorbachev, Mohammed Bouazizi, Nash equilibrium, Nate Silver, Nelson Mandela, obamacare, operational security, pattern recognition, performance metric, Pierre-Simon Laplace, place-making, placebo effect, precautionary principle, prediction markets, quantitative easing, random walk, randomized controlled trial, Richard Feynman, Richard Thaler, Robert Shiller, Ronald Reagan, Saturday Night Live, scientific worldview, Silicon Valley, Skype, statistical model, stem cell, Steve Ballmer, Steve Jobs, Steven Pinker, tacit knowledge, tail risk, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Watson beat the top human players on Jeopardy!

If he says, “It’s to the left,” the likelihood of the first ball being on the right side of the table increases a little more. Keep repeating the process and you slowly narrow the range of the possible locations, zeroing in on the truth—although you will never eliminate uncertainty entirely.16 If you’ve taken Statistics 101, you may recall a version of this thought experiment was dreamt up by Thomas Bayes. A Presbyterian minister, educated in logic, Bayes was born in 1701, so he lived at the dawn of modern probability theory, a subject to which he contributed with “An Essay Towards Solving a Problem in the Doctrine of Chances.” That essay, in combination with the work of Bayes’ friend Richard Price, who published Bayes’ essay posthumously in 1761, and the insights of the great French mathematician Pierre-Simon Laplace, ultimately produced Bayes’ theorem.

Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It) by William Poundstone

affirmative action, Albert Einstein, book value, business cycle, Debian, democratizing finance, desegregation, Donald Trump, en.wikipedia.org, Everything should be made as simple as possible, global village, guest worker program, guns versus butter model, hiring and firing, illegal immigration, invisible hand, jimmy wales, John Nash: game theory, John von Neumann, Kenneth Arrow, manufacturing employment, Nash equilibrium, Paul Samuelson, Pierre-Simon Laplace, prisoner's dilemma, Ralph Nader, RAND corporation, Ronald Reagan, Silicon Valley, slashdot, the map is not the territory, Thomas Bayes, Tragedy of the Commons, transcontinental railway, Unsafe at Any Speed, Y2K

Smith holds or has applied for patents covering such exotica as a computer made out of DNA, theft-proof credit cards, a 3-D vision process, and a magnetic catapult that could be used for launching satellites, In December 2000, with the Supreme Court deciding a bitterly contested presidency, Smith completed an article purporting to demonstrate the superiority of a system that no one had taken seriously, range voting. He began with an idea for comparing the merits of different voting systems, using a measure called Bayesian regret. The "Bayes" part refers to eighteenth-century English mathematician Thomas Bayes, a pioneer of probability theory, "Bayesian regret" is a statistical term that Smith defines as "expected avoidable human unhappiness." In other words, Smith tried to gauge how voting systems fail the voters by electing candidates other than the one who would have resulted in the greatest overall satisfaction, To do this, he ran a large series of computer simulations of elections.

The Knowledge Machine: How Irrationality Created Modern Science by Michael Strevens

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, Atul Gawande, coronavirus, COVID-19, dark matter, data science, Eddington experiment, Edmond Halley, Fellow of the Royal Society, fudge factor, germ theory of disease, Great Leap Forward, Gregor Mendel, heat death of the universe, Higgs boson, Intergovernmental Panel on Climate Change (IPCC), invention of movable type, invention of the telescope, Isaac Newton, Islamic Golden Age, Johannes Kepler, Large Hadron Collider, longitudinal study, Louis Pasteur, military-industrial complex, Murray Gell-Mann, Peace of Westphalia, Richard Feynman, Stephen Hawking, Steven Pinker, systematic bias, Thales of Miletus, the scientific method, Thomas Bayes, William of Occam

Philosophers call it (I’m sorry to say) “confirmation holism.” 83 The heart of scientific logic is a human heart: To more precisely formulate these ideas, philosophers have constructed probabilistic logics to capture scientists’ plausibility rankings and their role in evaluating evidence. Such logical systems differ in various ways, but they all implement to some extent a simple idea: if your chain breaks, suspect the weakest link. The most influential probabilistic system was first developed by the eighteenth-century clergyman and mathematician Thomas Bayes (1701–1761). Bayes’s approach cannot be wholly correct—it assumes that scientists know all possible theories in advance—but it provides an excellent model of many aspects of scientific inquiry. In the Bayesian framework, scientists’ plausibility rankings for the things that matter—hypotheses and auxiliary assumptions—are represented by numbers between 0 and 1, varying from person to person.

The Road to Conscious Machines by Michael Wooldridge

Ada Lovelace, AI winter, algorithmic bias, AlphaGo, Andrew Wiles, Anthropocene, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, backpropagation, basic income, Bletchley Park, Boeing 747, British Empire, call centre, Charles Babbage, combinatorial explosion, computer vision, Computing Machinery and Intelligence, DARPA: Urban Challenge, deep learning, deepfake, DeepMind, Demis Hassabis, don't be evil, Donald Trump, driverless car, Elaine Herzberg, Elon Musk, Eratosthenes, factory automation, fake news, future of work, gamification, general purpose technology, Geoffrey Hinton, gig economy, Google Glasses, intangible asset, James Watt: steam engine, job automation, John von Neumann, Loebner Prize, Minecraft, Mustafa Suleyman, Nash equilibrium, Nick Bostrom, Norbert Wiener, NP-complete, P = NP, P vs NP, paperclip maximiser, pattern recognition, Philippa Foot, RAND corporation, Ray Kurzweil, Rodney Brooks, self-driving car, Silicon Valley, Stephen Hawking, Steven Pinker, strong AI, technological singularity, telemarketer, Tesla Model S, The Coming Technological Singularity, The Future of Employment, the scientific method, theory of mind, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, trolley problem, Turing machine, Turing test, universal basic income, Von Neumann architecture, warehouse robotics

Many ad hoc schemes for dealing with uncertainty were invented and re-invented throughout the history of AI, but by the 1990s, one approach had come to dominate. The approach is called Bayesian inference. Bayesian inference was invented by an eighteenth-century British mathematician, the Reverend Thomas Bayes. He formulated a version of a technique that we now call Bayes’ Theorem in his honour. It is concerned with how we should rationally adjust our beliefs in the presence of new information. In the case of our driverless car example, the beliefs relate to whether there is an obstacle in front of us; the new information is the sensor data.

The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis by James Rickards

"World Economic Forum" Davos, Affordable Care Act / Obamacare, Alan Greenspan, Albert Einstein, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, Bayesian statistics, Bear Stearns, behavioural economics, Ben Bernanke: helicopter money, Benoit Mandelbrot, Berlin Wall, Bernie Sanders, Big bang: deregulation of the City of London, bitcoin, Black Monday: stock market crash in 1987, Black Swan, blockchain, Boeing 747, Bonfire of the Vanities, Bretton Woods, Brexit referendum, British Empire, business cycle, butterfly effect, buy and hold, capital controls, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, cellular automata, cognitive bias, cognitive dissonance, complexity theory, Corn Laws, corporate governance, creative destruction, Credit Default Swap, cuban missile crisis, currency manipulation / currency intervention, currency peg, currency risk, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, debt deflation, Deng Xiaoping, disintermediation, distributed ledger, diversification, diversified portfolio, driverless car, Edward Lorenz: Chaos theory, Eugene Fama: efficient market hypothesis, failed state, Fall of the Berlin Wall, fiat currency, financial repression, fixed income, Flash crash, floating exchange rates, forward guidance, Fractional reserve banking, G4S, George Akerlof, Glass-Steagall Act, global macro, global reserve currency, high net worth, Hyman Minsky, income inequality, information asymmetry, interest rate swap, Isaac Newton, jitney, John Meriwether, John von Neumann, Joseph Schumpeter, junk bonds, Kenneth Rogoff, labor-force participation, large denomination, liquidity trap, Long Term Capital Management, low interest rates, machine readable, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, Minsky moment, Money creation, money market fund, mutually assured destruction, Myron Scholes, Naomi Klein, nuclear winter, obamacare, offshore financial centre, operational security, Paul Samuelson, Peace of Westphalia, Phillips curve, Pierre-Simon Laplace, plutocrats, prediction markets, price anchoring, price stability, proprietary trading, public intellectual, quantitative easing, RAND corporation, random walk, reserve currency, RFID, risk free rate, risk-adjusted returns, Robert Solow, Ronald Reagan, Savings and loan crisis, Silicon Valley, sovereign wealth fund, special drawing rights, stock buybacks, stocks for the long run, tech billionaire, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transfer pricing, value at risk, Washington Consensus, We are all Keynesians now, Westphalian system

Investors who use complexity theory can leave mainstream analysis behind and get better forecasting results. The third tool in addition to behavioral psychology and complexity theory is Bayesian statistics, a branch of etiology also referred to as causal inference. Both terms derive from Bayes’ theorem, an equation first described by Thomas Bayes and published posthumously in 1763. A version of the theorem was elaborated independently and more formally by the French mathematician Pierre-Simon Laplace in 1774. Laplace continued work on the theorem in subsequent decades. Twentieth-century statisticians have developed more rigorous forms.

Programming Collective Intelligence by Toby Segaran

algorithmic management, always be closing, backpropagation, correlation coefficient, Debian, en.wikipedia.org, Firefox, full text search, functional programming, information retrieval, PageRank, prediction markets, recommendation engine, slashdot, social bookmarking, sparse data, Thomas Bayes, web application

In docclass.py, create a subclass of classifier called naivebayes, and create a docprob method that extracts the features (words) and multiplies all their probabilities together to get an overall probability: class naivebayes(classifier): def docprob(self,item,cat): features=self.getfeatures(item) # Multiply the probabilities of all the features together p=1 for f in features: p*=self.weightedprob(f,cat,self.fprob) return p You now know how to calculate Pr(Document | Category), but this isn't very useful by itself. In order to classify documents, you really need Pr(Category | Document). In other words, given a specific document, what's the probability that it fits into this category? Fortunately, a British mathematician named Thomas Bayes figured out how to do this about 250 years ago. A Quick Introduction to Bayes' Theorem Bayes' Theorem is a way of flipping around conditional probabilities. It's usually written as: Pr(A | B) = Pr(B | A) × Pr(A)/Pr(B) In the example, this becomes: Pr(Category | Document) = Pr(Document | Category) × Pr(Category) / Pr(Document) The previous section showed how to calculate Pr(Document | Category), but what about the other two values in the equation?

The Deep Learning Revolution (The MIT Press) by Terrence J. Sejnowski

AI winter, Albert Einstein, algorithmic bias, algorithmic trading, AlphaGo, Amazon Web Services, Any sufficiently advanced technology is indistinguishable from magic, augmented reality, autonomous vehicles, backpropagation, Baxter: Rethink Robotics, behavioural economics, bioinformatics, cellular automata, Claude Shannon: information theory, cloud computing, complexity theory, computer vision, conceptual framework, constrained optimization, Conway's Game of Life, correlation does not imply causation, crowdsourcing, Danny Hillis, data science, deep learning, DeepMind, delayed gratification, Demis Hassabis, Dennis Ritchie, discovery of DNA, Donald Trump, Douglas Engelbart, driverless car, Drosophila, Elon Musk, en.wikipedia.org, epigenetics, Flynn Effect, Frank Gehry, future of work, Geoffrey Hinton, Google Glasses, Google X / Alphabet X, Guggenheim Bilbao, Gödel, Escher, Bach, haute couture, Henri Poincaré, I think there is a world market for maybe five computers, industrial robot, informal economy, Internet of things, Isaac Newton, Jim Simons, John Conway, John Markoff, John von Neumann, language acquisition, Large Hadron Collider, machine readable, Mark Zuckerberg, Minecraft, natural language processing, Neil Armstrong, Netflix Prize, Norbert Wiener, OpenAI, orbital mechanics / astrodynamics, PageRank, pattern recognition, pneumatic tube, prediction markets, randomized controlled trial, Recombinant DNA, recommendation engine, Renaissance Technologies, Rodney Brooks, self-driving car, Silicon Valley, Silicon Valley startup, Socratic dialogue, speech recognition, statistical model, Stephen Hawking, Stuart Kauffman, theory of mind, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, Turing machine, Von Neumann architecture, Watson beat the top human players on Jeopardy!, world market for maybe five computers, X Prize, Yogi Berra

Tomaso Poggio had developed a hierarchical network called “HMAX” that could classify a limited number of objects.2 This suggested that performance would improve with deeper networks. In the first years of the new century, graphical models were developed that made contact with a rich vein of probabilistic models called “Bayes networks,” based on a theorem formulated by the eighteenth-century British mathematician Thomas Bayes that allows new evidence to update prior beliefs. Judea Pearl at the University of California, Los Angeles, had earlier introduced “belief networks”3 to artificial intelligence based on Bayesian analysis, which were strengthened and extended by developing methods for learning the probabilities in the networks from data.

The Devil's Derivatives: The Untold Story of the Slick Traders and Hapless Regulators Who Almost Blew Up Wall Street . . . And Are Ready to Do It Again by Nicholas Dunbar

Alan Greenspan, asset-backed security, bank run, banking crisis, Basel III, Bear Stearns, behavioural economics, Black Swan, Black-Scholes formula, bonus culture, book value, break the buck, buy and hold, capital asset pricing model, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, commoditize, Credit Default Swap, credit default swaps / collateralized debt obligations, currency risk, delayed gratification, diversification, Edmond Halley, facts on the ground, fear index, financial innovation, fixed income, George Akerlof, Glass-Steagall Act, Greenspan put, implied volatility, index fund, interest rate derivative, interest rate swap, Isaac Newton, John Meriwether, junk bonds, Kenneth Rogoff, Kickstarter, Long Term Capital Management, margin call, market bubble, money market fund, Myron Scholes, Nick Leeson, Northern Rock, offshore financial centre, Paul Samuelson, price mechanism, proprietary trading, regulatory arbitrage, rent-seeking, Richard Thaler, risk free rate, risk tolerance, risk/return, Ronald Reagan, Salesforce, Savings and loan crisis, seminal paper, shareholder value, short selling, statistical model, subprime mortgage crisis, The Chicago School, Thomas Bayes, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, yield curve, zero-sum game

One might argue that since the market values the loans at $800 million, the bank ought to write down the value of the equity investment to zero. However, accounting rules for loan books don’t require such recognitions to take place. 7. After de Moivre’s death, the refinement of mortality calculations was continued in London by Richard Price, friend of Thomas Bayes and Benjamin Franklin, and founding actuary of the Equitable Life Assurance Society. 8. Arturo Cifuentes and Gerard O’Connor, “The Binomial Expansion Method Applied to CBO/CLO Analysis,” Moody’s Investors Service special report, December 13, 1996. 9. Ibid. 10. For a detailed account of the invention of BISTRO, see Gillian Tett, Fool’s Gold: How the Bold Dream of a Small Tribe at J.P.

The Skeptical Economist: Revealing the Ethics Inside Economics by Jonathan Aldred

airport security, behavioural economics, Berlin Wall, carbon credits, carbon footprint, citizen journalism, clean water, cognitive dissonance, congestion charging, correlation does not imply causation, Diane Coyle, endogenous growth, experimental subject, Fall of the Berlin Wall, first-past-the-post, framing effect, Goodhart's law, GPS: selective availability, greed is good, happiness index / gross national happiness, hedonic treadmill, Intergovernmental Panel on Climate Change (IPCC), invisible hand, job satisfaction, John Maynard Keynes: Economic Possibilities for our Grandchildren, labour market flexibility, laissez-faire capitalism, libertarian paternalism, longitudinal study, new economy, Paradox of Choice, Pareto efficiency, pension reform, positional goods, precautionary principle, price elasticity of demand, Ralph Waldo Emerson, RAND corporation, risk tolerance, school choice, social discount rate, spectrum auction, Thomas Bayes, trade liberalization, ultimatum game, When a measure becomes a target

This is a very broad question, so we shall focus on just one aspect of it, namely the practice of quantifying uncertainty and ignorance — inventing probabilities when there is no basis to do so. The practice is widespread among economists because many of them believe that, no matter how extreme the uncertainty, effective probabilities always exist. This view is termed ‘subjective Bayesianism’ (hereafter Bayesianism for short), from the Reverend Thomas Bayes, an 18th-century English mathematician.35 Its implications are startling. Bayesians believe there is no such thing as pure uncertainty in the sense I have defined it. They assert that we always use probabilities, consciously or otherwise, when outcomes are not certain. The issues are more clearly depicted in simple gambling games than messy real-world choices; the Ellsberg Paradox (see box opposite) is a classic illustration.

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman

affirmative action, Affordable Care Act / Obamacare, Alan Greenspan, Albert Einstein, Andrew Wiles, automated trading system, backtesting, Bayesian statistics, Bear Stearns, beat the dealer, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black Monday: stock market crash in 1987, blockchain, book value, Brownian motion, butter production in bangladesh, buy and hold, buy low sell high, Cambridge Analytica, Carl Icahn, Claude Shannon: information theory, computer age, computerized trading, Credit Default Swap, Daniel Kahneman / Amos Tversky, data science, diversified portfolio, Donald Trump, Edward Thorp, Elon Musk, Emanuel Derman, endowment effect, financial engineering, Flash crash, George Gilder, Gordon Gekko, illegal immigration, index card, index fund, Isaac Newton, Jim Simons, John Meriwether, John Nash: game theory, John von Neumann, junk bonds, Loma Prieta earthquake, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, Mark Zuckerberg, Michael Milken, Monty Hall problem, More Guns, Less Crime, Myron Scholes, Naomi Klein, natural language processing, Neil Armstrong, obamacare, off-the-grid, p-value, pattern recognition, Peter Thiel, Ponzi scheme, prediction markets, proprietary trading, quantitative hedge fund, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, Robert Mercer, Ronald Reagan, self-driving car, Sharpe ratio, Silicon Valley, sovereign wealth fund, speech recognition, statistical arbitrage, statistical model, Steve Bannon, Steve Jobs, stochastic process, the scientific method, Thomas Bayes, transaction costs, Turing machine, Two Sigma

To do that, the IBM researchers employed the Baum-Welch algorithm—codeveloped by Jim Simons’s early trading partner Lenny Baum—to zero in on the various language probabilities. Rather than manually programming in static knowledge about how language worked, they created a program that learned from data. Brown, Mercer, and the others relied upon Bayesian mathematics, which had emerged from the statistical rule proposed by Reverend Thomas Bayes in the eighteenth-century. Bayesians will attach a degree of probability to every guess and update their best estimates as they receive new information. The genius of Bayesian statistics is that it continuously narrows a range of possibilities. Think, for example, of a spam filter, which doesn’t know with certainty if an email is malicious, but can be effective by assigning odds to each one received by constantly learning from emails previously classified as “junk.”

The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World by Pedro Domingos

Albert Einstein, Amazon Mechanical Turk, Arthur Eddington, backpropagation, basic income, Bayesian statistics, Benoit Mandelbrot, bioinformatics, Black Swan, Brownian motion, cellular automata, Charles Babbage, Claude Shannon: information theory, combinatorial explosion, computer vision, constrained optimization, correlation does not imply causation, creative destruction, crowdsourcing, Danny Hillis, data is not the new oil, data is the new oil, data science, deep learning, DeepMind, double helix, Douglas Hofstadter, driverless car, Erik Brynjolfsson, experimental subject, Filter Bubble, future of work, Geoffrey Hinton, global village, Google Glasses, Gödel, Escher, Bach, Hans Moravec, incognito mode, information retrieval, Jeff Hawkins, job automation, John Markoff, John Snow's cholera map, John von Neumann, Joseph Schumpeter, Kevin Kelly, large language model, lone genius, machine translation, mandelbrot fractal, Mark Zuckerberg, Moneyball by Michael Lewis explains big data, Narrative Science, Nate Silver, natural language processing, Netflix Prize, Network effects, Nick Bostrom, NP-complete, off grid, P = NP, PageRank, pattern recognition, phenotype, planetary scale, power law, pre–internet, random walk, Ray Kurzweil, recommendation engine, Richard Feynman, scientific worldview, Second Machine Age, self-driving car, Silicon Valley, social intelligence, speech recognition, Stanford marshmallow experiment, statistical model, Stephen Hawking, Steven Levy, Steven Pinker, superintelligent machines, the long tail, the scientific method, The Signal and the Noise by Nate Silver, theory of mind, Thomas Bayes, transaction costs, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, white flight, yottabyte, zero-sum game

For Bayesians, learning is “just” another application of Bayes’ theorem, with whole models as the hypotheses and the data as the evidence: as you see more data, some models become more likely and some less, until ideally one model stands out as the clear winner. Bayesians have invented fiendishly clever kinds of models. So let’s get started. Thomas Bayes was an eighteenth-century English clergyman who, without realizing it, became the center of a new religion. You may well ask how that could happen, until you notice that it happened to Jesus, too: Christianity as we know it was invented by Saint Paul, while Jesus saw himself as the pinnacle of the Jewish faith.

The Undoing Project: A Friendship That Changed Our Minds by Michael Lewis

Albert Einstein, availability heuristic, behavioural economics, Cass Sunstein, choice architecture, complexity theory, Daniel Kahneman / Amos Tversky, Donald Trump, Douglas Hofstadter, endowment effect, feminist movement, framing effect, hindsight bias, John von Neumann, Kenneth Arrow, Linda problem, loss aversion, medical residency, Menlo Park, Murray Gell-Mann, Nate Silver, New Journalism, Paul Samuelson, peak-end rule, Richard Thaler, Saturday Night Live, Skinner box, Stanford marshmallow experiment, statistical model, systematic bias, the new new thing, Thomas Bayes, Walter Mischel, Yom Kippur War

After extracting each chip, he’d give the psychologists his best guess of the odds that the bag he was holding was filled with mostly red, or mostly white, chips. The beauty of the experiment was that there was a correct answer to the question: What is the probability that I am holding the bag of mostly red chips? It was provided by a statistical formula called Bayes’s theorem (after Thomas Bayes, who, strangely, left the formula for others to discover in his papers after his death, in 1761). Bayes’s rule allowed you to calculate the true odds, after each new chip was pulled from it, that the book bag in question was the one with majority white, or majority red, chips. Before any chips had been withdrawn, those odds were 50:50—the bag in your hands was equally likely to be either majority red or majority white.

The Digital Doctor: Hope, Hype, and Harm at the Dawn of Medicine’s Computer Age by Robert Wachter

activist fund / activist shareholder / activist investor, Affordable Care Act / Obamacare, AI winter, Airbnb, Atul Gawande, Captain Sullenberger Hudson, Checklist Manifesto, Chuck Templeton: OpenTable:, Clayton Christensen, cognitive load, collapse of Lehman Brothers, computer age, creative destruction, crowdsourcing, deep learning, deskilling, disruptive innovation, driverless car, en.wikipedia.org, Erik Brynjolfsson, everywhere but in the productivity statistics, Firefox, Frank Levy and Richard Murnane: The New Division of Labor, general purpose technology, Google Glasses, human-factors engineering, hype cycle, Ignaz Semmelweis: hand washing, Internet of things, job satisfaction, Joseph Schumpeter, Kickstarter, knowledge worker, lifelogging, Marc Benioff, medical malpractice, medical residency, Menlo Park, minimum viable product, natural language processing, Network effects, Nicholas Carr, obamacare, pattern recognition, peer-to-peer, personalized medicine, pets.com, pneumatic tube, Productivity paradox, Ralph Nader, RAND corporation, Richard Hendricks, Robert Solow, Salesforce, Second Machine Age, self-driving car, seminal paper, Silicon Valley, Silicon Valley startup, six sigma, Skype, Snapchat, software as a service, Steve Jobs, Steven Levy, TED Talk, The future is already here, the payments system, The Wisdom of Crowds, Thomas Bayes, Toyota Production System, Uber for X, US Airways Flight 1549, Watson beat the top human players on Jeopardy!, Yogi Berra

This is the part of diagnostic reasoning that beginners find most vexing, since they lack the foundational knowledge to understand why their teacher focused so intently on one nugget of information and all but ignored others that, to the novice, seemed equally crucial. How do the great diagnosticians make such choices? We now recognize this as a relatively intuitive version of Bayes’ theorem. Developed by the eighteenth-century British theologian-turned-mathematician Thomas Bayes, this theorem (often ignored by students because it is taught to them with the dryness of a Passover matzo) is the linchpin of clinical reasoning. In essence, Bayes’ theorem says that any medical test must be interpreted from two perspectives. The first: How accurate is the test—that is, how often does it give right or wrong answers?

Human Frontiers: The Future of Big Ideas in an Age of Small Thinking by Michael Bhaskar

"Margaret Hamilton" Apollo, 3D printing, additive manufacturing, AI winter, Albert Einstein, algorithmic trading, AlphaGo, Anthropocene, artificial general intelligence, augmented reality, autonomous vehicles, backpropagation, barriers to entry, basic income, behavioural economics, Benoit Mandelbrot, Berlin Wall, Big bang: deregulation of the City of London, Big Tech, Bletchley Park, blockchain, Boeing 747, brain emulation, Brexit referendum, call centre, carbon tax, charter city, citizen journalism, Claude Shannon: information theory, Clayton Christensen, clean tech, clean water, cognitive load, Columbian Exchange, coronavirus, cosmic microwave background, COVID-19, creative destruction, CRISPR, crony capitalism, cyber-physical system, dark matter, David Graeber, deep learning, DeepMind, deindustrialization, dematerialisation, Demis Hassabis, demographic dividend, Deng Xiaoping, deplatforming, discovery of penicillin, disruptive innovation, Donald Trump, double entry bookkeeping, Easter island, Edward Jenner, Edward Lorenz: Chaos theory, Elon Musk, en.wikipedia.org, endogenous growth, energy security, energy transition, epigenetics, Eratosthenes, Ernest Rutherford, Eroom's law, fail fast, false flag, Fellow of the Royal Society, flying shuttle, Ford Model T, Francis Fukuyama: the end of history, general purpose technology, germ theory of disease, glass ceiling, global pandemic, Goodhart's law, Google Glasses, Google X / Alphabet X, GPT-3, Haber-Bosch Process, hedonic treadmill, Herman Kahn, Higgs boson, hive mind, hype cycle, Hyperloop, Ignaz Semmelweis: hand washing, Innovator's Dilemma, intangible asset, interchangeable parts, Internet of things, invention of agriculture, invention of the printing press, invention of the steam engine, invention of the telegraph, invisible hand, Isaac Newton, ITER tokamak, James Watt: steam engine, James Webb Space Telescope, Jeff Bezos, jimmy wales, job automation, Johannes Kepler, John von Neumann, Joseph Schumpeter, Kenneth Arrow, Kevin Kelly, Kickstarter, knowledge economy, knowledge worker, Large Hadron Collider, liberation theology, lockdown, lone genius, loss aversion, Louis Pasteur, Mark Zuckerberg, Martin Wolf, megacity, megastructure, Menlo Park, Minecraft, minimum viable product, mittelstand, Modern Monetary Theory, Mont Pelerin Society, Murray Gell-Mann, Mustafa Suleyman, natural language processing, Neal Stephenson, nuclear winter, nudge unit, oil shale / tar sands, open economy, OpenAI, opioid epidemic / opioid crisis, PageRank, patent troll, Peter Thiel, plutocrats, post scarcity, post-truth, precautionary principle, public intellectual, publish or perish, purchasing power parity, quantum entanglement, Ray Kurzweil, remote working, rent-seeking, Republic of Letters, Richard Feynman, Robert Gordon, Robert Solow, secular stagnation, shareholder value, Silicon Valley, Silicon Valley ideology, Simon Kuznets, skunkworks, Slavoj Žižek, sovereign wealth fund, spinning jenny, statistical model, stem cell, Steve Jobs, Stuart Kauffman, synthetic biology, techlash, TED Talk, The Rise and Fall of American Growth, the scientific method, The Wealth of Nations by Adam Smith, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, TikTok, total factor productivity, transcontinental railway, Two Sigma, Tyler Cowen, Tyler Cowen: Great Stagnation, universal basic income, uranium enrichment, We wanted flying cars, instead we got 140 characters, When a measure becomes a target, X Prize, Y Combinator

What he'd built was a miniature factory for ideas: in Edison's words it was for ‘rapid and cheap development of an invention’, nothing less than ‘a minor invention every ten days and a big thing every six months or so’. It was precisely the system, the network, the organisation, that had become significant. In the early nineteenth century a painter like Samuel Morse could still invent the telegraph. Lone scribblers and tinkerers were common – English reverends like Thomas Bayes, gentleman thinkers like Darwin, renegades and loners from Nietzsche to Marconi. But while inventions like the telephone, radio and the motor car were still associated with individuals (even if in reality many individuals were about to realise them), each had quickly led to the growth of behemoths like Bell Corporation, RCA or General Motors.

Little Brother by Cory Doctorow

Aaron Swartz, airport security, Bayesian statistics, Berlin Wall, citizen journalism, Firefox, game design, Golden Gate Park, Haight Ashbury, Internet Archive, Isaac Newton, Jane Jacobs, Jeff Bezos, John Gilmore, John Perry Barlow, mail merge, Mitch Kapor, MITM: man-in-the-middle, Neal Stephenson, RFID, San Francisco homelessness, Sand Hill Road, Silicon Valley, slashdot, Steve Jobs, Steve Wozniak, Thomas Bayes, web of trust, zero day

No one could tell which of the Internet's packets were Xnet and which ones were just plain old banking and e-commerce and other encrypted communication. You couldn't find out who was tying the Xnet, let alone who was using the Xnet. But what about Dad's "Bayesian statistics?" I'd played with Bayesian math before. Darryl and I once tried to write our own better spam filter and when you filter spam, you need Bayesian math. Thomas Bayes was an 18th century British mathematician that no one cared about until a couple hundred years after he died, when computer scientists realized that his technique for statistically analyzing mountains of data would be super-useful for the modern world's info-Himalayas. Here's some of how Bayesian stats work.

Statistics hacks by Bruce Frey

Bayesian statistics, Berlin Wall, correlation coefficient, Daniel Kahneman / Amos Tversky, distributed generation, en.wikipedia.org, feminist movement, G4S, game design, Hacker Ethic, index card, Linda problem, Milgram experiment, Monty Hall problem, p-value, place-making, reshoring, RFID, Search for Extraterrestrial Intelligence, SETI@home, Silicon Valley, statistical model, sugar pill, systematic bias, Thomas Bayes

Of the 9,102 women who will score negative on the screening, 12 actually have cancer. This is a relatively small 1/10 of 1 percent, but the testing will miss those people altogether, and they will not receive treatment. Why It Works Medical screening accuracy uses a specific application of a generalized approach to conditional probability attributed to Thomas Bayes, a philosopher and mathematician in the 1700s. "If this, then what are the chances that..." is a conditional probability question. Bayes's approach to conditional probabilities was to look at the naturally occurring frequencies of events. The basic formula for estimating the chance that one has a disease if one has a positive test result is: Expressed as conditional probabilities, the formula is: To answer the all-important question in our breast cancer example ("If a woman scores a positive test result, how likely is she to have breast cancer?")

Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander

asset allocation, backtesting, barriers to entry, Brownian motion, capital asset pricing model, constrained optimization, credit crunch, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial engineering, fixed income, implied volatility, interest rate swap, low interest rates, market friction, market microstructure, p-value, performance metric, power law, proprietary trading, quantitative trading / quantitative finance, random walk, risk free rate, risk tolerance, risk-adjusted returns, risk/return, seminal paper, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, systematic bias, Thomas Bayes, transaction costs, two and twenty, value at risk, volatility smile, Wiener process, yield curve, zero-sum game

Thus, because we observe that there is 1 chance in 6 of getting a five when a fair die is thrown, we say that the probability of this event is 1/6. But long before the relative frequentist theory came to dominate our approach to probability and statistics, a more general Bayesian approach to probability and statistics had been pioneered by Thomas Bayes (1702–1761). The classical approach is based on objective information culled from experimental observations, but Bayes allowed subjective assessments of probabilities to be made, calling these assessments the prior beliefs. In fact, the classical approach is just a simple case of Bayesian probability and statistics, where there is no subjective information and so the prior distribution is uniform.

The Ascent of Money: A Financial History of the World by Niall Ferguson

Admiral Zheng, Alan Greenspan, An Inconvenient Truth, Andrei Shleifer, Asian financial crisis, asset allocation, asset-backed security, Atahualpa, bank run, banking crisis, banks create money, Bear Stearns, Black Monday: stock market crash in 1987, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, BRICs, British Empire, business cycle, capital asset pricing model, capital controls, Carmen Reinhart, Cass Sunstein, central bank independence, classic study, collateralized debt obligation, colonial exploitation, commoditize, Corn Laws, corporate governance, creative destruction, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, deglobalization, diversification, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Glaeser, Edward Lloyd's coffeehouse, equity risk premium, financial engineering, financial innovation, financial intermediation, fixed income, floating exchange rates, Fractional reserve banking, Francisco Pizarro, full employment, Future Shock, German hyperinflation, Greenspan put, Herman Kahn, Hernando de Soto, high net worth, hindsight bias, Home mortgage interest deduction, Hyman Minsky, income inequality, information asymmetry, interest rate swap, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, iterative process, James Carville said: "I would like to be reincarnated as the bond market. You can intimidate everybody.", John Meriwether, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, junk bonds, Kenneth Arrow, Kenneth Rogoff, knowledge economy, labour mobility, Landlord’s Game, liberal capitalism, London Interbank Offered Rate, Long Term Capital Management, low interest rates, market bubble, market fundamentalism, means of production, Mikhail Gorbachev, Modern Monetary Theory, Money creation, money market fund, money: store of value / unit of account / medium of exchange, moral hazard, mortgage debt, mortgage tax deduction, Myron Scholes, Naomi Klein, National Debt Clock, negative equity, Nelson Mandela, Nick Bostrom, Nick Leeson, Northern Rock, Parag Khanna, pension reform, price anchoring, price stability, principal–agent problem, probability theory / Blaise Pascal / Pierre de Fermat, profit motive, quantitative hedge fund, RAND corporation, random walk, rent control, rent-seeking, reserve currency, Richard Thaler, risk free rate, Robert Shiller, rolling blackouts, Ronald Reagan, Savings and loan crisis, savings glut, seigniorage, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spice trade, stocks for the long run, structural adjustment programs, subprime mortgage crisis, tail risk, technology bubble, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, Thomas Malthus, Thorstein Veblen, tontine, too big to fail, transaction costs, two and twenty, undersea cable, value at risk, W. E. B. Du Bois, Washington Consensus, Yom Kippur War

In 1738 the Swiss mathematician Daniel Bernoulli proposed that ‘The value of an item must not be based on its price, but rather on the utility that it yields’, and that the ‘utility resulting from any small increase in wealth will be inversely proportionate to the quantity of goods previously possessed’ - in other words $100 is worth more to someone on the median income than to a hedge fund manager. 6. Inference. In his ‘Essay Towards Solving a Problem in the Doctrine of Chances’ (published posthumously in 1764), Thomas Bayes set himself the following problem: ‘Given the number of times in which an unknown event has happened and failed; Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named.’ His resolution of the problem - ‘The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the chance of the thing expected upon it’s [sic] happening’ - anticipates the modern formulation that expected utility is the probability of an event times the payoff received in case of that event.18 In short, it was not merchants but mathematicians who were the true progenitors of modern insurance.

Entangled Life: How Fungi Make Our Worlds, Change Our Minds & Shape Our Futures by Merlin Sheldrake

Anthropocene, Apollo 11, biofilm, buy low sell high, carbon footprint, CRISPR, crowdsourcing, cuban missile crisis, dark matter, deep learning, discovery of penicillin, Easter island, experimental subject, Fellow of the Royal Society, Isaac Newton, Kickstarter, late capitalism, low earth orbit, Mason jar, meta-analysis, microbiome, moral panic, NP-complete, phenotype, randomized controlled trial, Ronald Reagan, seminal paper, TED Talk, the built environment, Thomas Bayes, Thomas Malthus, traveling salesman, two and twenty

sophistications of fungal lives: For estimates of the number of fungal species see Hawksworth (2001) and Hawksworth and Lücking (2017). when we actually look: Among neuroscientists, the involvement of our expectations in perception is known as top-down influence, or sometimes as Bayesian inference (after Thomas Bayes, a mathematician who made a founding contribution to the mathematics of probability, or “the doctrine of chances”). See Gilbert and Sigman (2007), and Mazzucato et al. (2019). “they’re cleverer than me”: Adamatzky (2016), Latty and Beekman (2011), Nakagaki et al. (2000), Bonifaci et al. (2012), Tero et al. (2010), and Oettmeier et al. (2017).

Rationality: What It Is, Why It Seems Scarce, Why It Matters by Steven Pinker

affirmative action, Albert Einstein, autonomous vehicles, availability heuristic, Ayatollah Khomeini, backpropagation, basic income, behavioural economics, belling the cat, Black Lives Matter, butterfly effect, carbon tax, Cass Sunstein, choice architecture, classic study, clean water, Comet Ping Pong, coronavirus, correlation coefficient, correlation does not imply causation, COVID-19, critical race theory, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, data science, David Attenborough, deep learning, defund the police, delayed gratification, disinformation, Donald Trump, Dr. Strangelove, Easter island, effective altruism, en.wikipedia.org, Erdős number, Estimating the Reproducibility of Psychological Science, fake news, feminist movement, framing effect, George Akerlof, George Floyd, germ theory of disease, high batting average, if you see hoof prints, think horses—not zebras, index card, Jeff Bezos, job automation, John Nash: game theory, John von Neumann, libertarian paternalism, Linda problem, longitudinal study, loss aversion, Mahatma Gandhi, meta-analysis, microaggression, Monty Hall problem, Nash equilibrium, New Journalism, Paul Erdős, Paul Samuelson, Peter Singer: altruism, Pierre-Simon Laplace, placebo effect, post-truth, power law, QAnon, QWERTY keyboard, Ralph Waldo Emerson, randomized controlled trial, replication crisis, Richard Thaler, scientific worldview, selection bias, social discount rate, social distancing, Social Justice Warrior, Stanford marshmallow experiment, Steve Bannon, Steven Pinker, sunk-cost fallacy, TED Talk, the scientific method, Thomas Bayes, Tragedy of the Commons, trolley problem, twin studies, universal basic income, Upton Sinclair, urban planning, Walter Mischel, yellow journalism, zero-sum game

In chapters 6 and 7 we’ll explore how best to make consequential decisions when we know the probabilities, but the starting point must be the probabilities themselves: given the evidence, how likely is it that some state of affairs is true? For all the scariness of the word “theorem,” Bayes’s rule is rather simple, and as we will see at the end of the chapter, it can be made gut-level intuitive. The great insight of the Reverend Thomas Bayes (1701–1761) was that the degree of belief in a hypothesis may be quantified as a probability. (This is the subjectivist meaning of “probability” that we met in the last chapter.) Call it prob(Hypothesis), the probability of a hypothesis, that is, our degree of credence that it is true. (In the case of medical diagnosis, the hypothesis is that the patient has the disease.)

Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown, Eric Kim

Abraham Wald, activist fund / activist shareholder / activist investor, Albert Einstein, algorithmic trading, Asian financial crisis, Atul Gawande, backtesting, Basel III, Bayesian statistics, Bear Stearns, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Black Swan, book value, business cycle, capital asset pricing model, carbon tax, central bank independence, Checklist Manifesto, corporate governance, creative destruction, credit crunch, Credit Default Swap, currency risk, disintermediation, distributed generation, diversification, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, experimental subject, fail fast, fear index, financial engineering, financial innovation, global macro, illegal immigration, implied volatility, independent contractor, index fund, John Bogle, junk bonds, Long Term Capital Management, loss aversion, low interest rates, managed futures, margin call, market clearing, market fundamentalism, market microstructure, Money creation, money market fund, money: store of value / unit of account / medium of exchange, moral hazard, Myron Scholes, natural language processing, open economy, Pierre-Simon Laplace, power law, pre–internet, proprietary trading, quantitative trading / quantitative finance, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, shareholder value, Sharpe ratio, special drawing rights, statistical arbitrage, stochastic volatility, stock buybacks, stocks for the long run, tail risk, The Myth of the Rational Market, Thomas Bayes, too big to fail, transaction costs, value at risk, yield curve

Second, we know nothing about the accuracy of this statement in particular; we only make a claim about the long-term accuracy of lots of statements. This is how we turn an event that has already happened—drawing nine red marbles out of 10—into a hypothetical coin-flip gambling game that can be repeated indefinitely. The main alternative to frequentist statistics today is the Bayesian view. It is named for Thomas Bayes, an eighteenth-century theorist, but it was Pierre-Simon Laplace who put forth the basic ideas. It was not until the twentieth century, however, that researchers, including Richard Cox and Bruno de Finetti, created the modern formulation. In the Bayesian view of the urn, you must have some prior belief about the number of red marbles in the urn.

The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money by Steven Drobny

Albert Einstein, AOL-Time Warner, Asian financial crisis, asset allocation, asset-backed security, backtesting, banking crisis, Bear Stearns, Bernie Madoff, Black Swan, bond market vigilante , book value, Bretton Woods, BRICs, British Empire, business cycle, business process, buy and hold, capital asset pricing model, capital controls, central bank independence, collateralized debt obligation, commoditize, commodity super cycle, commodity trading advisor, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency peg, debt deflation, diversification, diversified portfolio, equity premium, equity risk premium, family office, fiat currency, fixed income, follow your passion, full employment, George Santayana, global macro, Greenspan put, Hyman Minsky, implied volatility, index fund, inflation targeting, interest rate swap, inventory management, inverted yield curve, invisible hand, junk bonds, Kickstarter, London Interbank Offered Rate, Long Term Capital Management, low interest rates, market bubble, market fundamentalism, market microstructure, Minsky moment, moral hazard, Myron Scholes, North Sea oil, open economy, peak oil, pension reform, Ponzi scheme, prediction markets, price discovery process, price stability, private sector deleveraging, profit motive, proprietary trading, purchasing power parity, quantitative easing, random walk, Reminiscences of a Stock Operator, reserve currency, risk free rate, risk tolerance, risk-adjusted returns, risk/return, savings glut, selection bias, Sharpe ratio, short selling, SoftBank, sovereign wealth fund, special drawing rights, statistical arbitrage, stochastic volatility, stocks for the long run, stocks for the long term, survivorship bias, tail risk, The Great Moderation, Thomas Bayes, time value of money, too big to fail, Tragedy of the Commons, transaction costs, two and twenty, unbiased observer, value at risk, Vanguard fund, yield curve, zero-sum game

We then input that adjusted expected return into the Titanic funnel, which assesses how much it will lose in a variety of cataclysms, giving me the recommended position. It is important to note that I am not putting trades on just to achieve the Titanic loss number. I am just looking for mispricings. Bayesian Methods The term Bayesian refers to the work Thomas Bayes, who proved a specific case of the now eponymous theorem, published after his death in 1761. The Bayesian interpretation of probability can be seen as a form of logic that allows for analysis of uncertain statements. To evaluate the probability of a hypothesis, Bayes’ theorem compares probabilities before and after the existence of new data.

Pirate Cinema by Cory Doctorow

airport security, citation needed, Internet Archive, place-making, QR code, retail therapy, smart cities, Thomas Bayes

He gestured at the rolling lawns to one side of the ancient, mossy, fenced-in headstones. "Nonconformist cemetery," he went on, leading me deeper. "Unconsecrated ground. Lots of interesting folks buried here. You got your writers: like John Bunyon who wrote Pilgrims Progress. You got your philosophers, like Thomas Hardy. And some real maths geniuses, like old Thomas Bayes --" He pointed to a low, mossy tomb. "He invented a branch of statistics that got built into every spam filter, a couple hundred years after they buried him." He sat down on a bench. It was after mid-day now, and only a few people were eating lunch around us, none close enough to overhear us.

The Human Cosmos: A Secret History of the Stars by Jo Marchant

Albert Einstein, Alfred Russel Wallace, Arthur Eddington, British Empire, complexity theory, Dava Sobel, Drosophila, Easter island, Eddington experiment, Edmond Halley, Eratosthenes, founder crops, game design, Great Leap Forward, Henri Poincaré, invention of writing, Isaac Newton, Johannes Kepler, John Harrison: Longitude, lateral thinking, Lewis Mumford, lone genius, mass immigration, meta-analysis, Nicholas Carr, out of africa, overview effect, Plato's cave, polynesian navigation, scientific mainstream, scientific worldview, Search for Extraterrestrial Intelligence, Searching for Interstellar Communications, Skype, social intelligence, Stephen Hawking, Steven Pinker, Stuart Kauffman, technological singularity, TED Talk, the scientific method, Thomas Bayes, trade route

He argues that treating information as a new kind of substance that exists in the external world, independent of our knowledge of it, was missing Wheeler’s point: “If a quantum state just was information, how could it be unknown? Surely it had to be known by someone or something?” Instead, Fuchs took inspiration from the Bayesian approach to probability (named for the eighteenth-century British mathematician Thomas Bayes). This argues that there are no objective probabilities out there to be discovered; when we determine the probability that a certain event will happen, it is always a function of our subjective knowledge and beliefs. Fuchs and his colleagues developed an analogous interpretation of quantum mechanics, which says that the probabilities calculated by quantum physicists relate not to what’s happening out in the world, but the internal knowledge of the observer.

Science Fictions: How Fraud, Bias, Negligence, and Hype Undermine the Search for Truth by Stuart Ritchie

Albert Einstein, anesthesia awareness, autism spectrum disorder, Bayesian statistics, Black Lives Matter, Carmen Reinhart, Cass Sunstein, Charles Babbage, citation needed, Climatic Research Unit, cognitive dissonance, complexity theory, coronavirus, correlation does not imply causation, COVID-19, crowdsourcing, data science, deindustrialization, Donald Trump, double helix, en.wikipedia.org, epigenetics, Estimating the Reproducibility of Psychological Science, fake news, Goodhart's law, Growth in a Time of Debt, Helicobacter pylori, Higgs boson, hype cycle, Kenneth Rogoff, l'esprit de l'escalier, Large Hadron Collider, meta-analysis, microbiome, Milgram experiment, mouse model, New Journalism, ocean acidification, p-value, phenotype, placebo effect, profit motive, publication bias, publish or perish, quantum entanglement, race to the bottom, randomized controlled trial, recommendation engine, rent-seeking, replication crisis, Richard Thaler, risk tolerance, Ronald Reagan, Scientific racism, selection bias, Silicon Valley, Silicon Valley startup, social distancing, Stanford prison experiment, statistical model, stem cell, Steven Pinker, TED Talk, Thomas Bayes, twin studies, Tyler Cowen, University of East Anglia, Wayback Machine

Doing away with p-values wouldn’t necessarily improve matters; in fact, by introducing another source of subjectivity, it might make the situation a lot worse.26 With tongue only partly in cheek, John Ioannidis has noted that if we remove all such objective measures we invite a situation where ‘all science will become like nutritional epidemiology’ – a scary prospect indeed.27 The same criticism is often levelled at the other main alternative to p-values: Bayesian statistics. Drawing on a probability theorem devised by the eighteenth-century statistician Thomas Bayes, this method allows researchers to take the strength of previous evidence – referred to as a ‘prior’ – into account when assessing the significance of new findings. For instance, if someone tells you their weather forecast predicts a rainy day in London in the autumn, it won’t take too much to convince you that they’re right.

From Bacteria to Bach and Back: The Evolution of Minds by Daniel C. Dennett

Ada Lovelace, adjacent possible, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, AlphaGo, Andrew Wiles, Bayesian statistics, bioinformatics, bitcoin, Bletchley Park, Build a better mousetrap, Claude Shannon: information theory, computer age, computer vision, Computing Machinery and Intelligence, CRISPR, deep learning, disinformation, double entry bookkeeping, double helix, Douglas Hofstadter, Elon Musk, epigenetics, experimental subject, Fermat's Last Theorem, Gödel, Escher, Bach, Higgs boson, information asymmetry, information retrieval, invention of writing, Isaac Newton, iterative process, John von Neumann, language acquisition, megaproject, Menlo Park, Murray Gell-Mann, Necker cube, Norbert Wiener, pattern recognition, phenotype, Richard Feynman, Rodney Brooks, self-driving car, social intelligence, sorting algorithm, speech recognition, Stephen Hawking, Steven Pinker, strong AI, Stuart Kauffman, TED Talk, The Wealth of Nations by Adam Smith, theory of mind, Thomas Bayes, trickle-down economics, Turing machine, Turing test, Watson beat the top human players on Jeopardy!, Y2K

With that caution in hand, we can address the idea that is now sweeping through cognitive science as a very promising answer to how the brain picks up, and uses, the available semantic information: Bayesian hierarchical predictive coding. (For excellent accounts see Hinton 2007; Clark 2013; and the commentary on Clark, Hohwy 2013.) The basic idea is delicious. The Reverend Thomas Bayes (1701–1761) developed a method of calculating probabilities based on one’s prior expectations. Each problem is couched thus: Given that your expectations based on past experience (including, we may add, the experience of your ancestors as passed down to you) are such and such (expressed as probabilities for each alternative), what effect on your future expectations should the following new data have?

How to Change Your Mind: What the New Science of Psychedelics Teaches Us About Consciousness, Dying, Addiction, Depression, and Transcendence by Michael Pollan

1960s counterculture, Abraham Maslow, Albert Einstein, Anton Chekhov, Burning Man, cognitive dissonance, conceptual framework, crowdsourcing, dark matter, Day of the Dead, Douglas Engelbart, East Village, experimental subject, Exxon Valdez, Golden Gate Park, Google Earth, Haight Ashbury, Howard Rheingold, Internet Archive, John Markoff, John Perry Barlow, Kevin Kelly, Marshall McLuhan, Mason jar, Menlo Park, meta-analysis, microdosing, military-industrial complex, moral panic, Mother of all demos, off-the-grid, overview effect, placebo effect, radical decentralization, Ralph Waldo Emerson, randomized controlled trial, reality distortion field, Ronald Reagan, Salesforce, satellite internet, scientific mainstream, scientific worldview, selective serotonin reuptake inhibitor (SSRI), sensible shoes, Silicon Valley, Skype, Steve Jobs, Stewart Brand, sugar pill, TED Talk, the scientific method, theory of mind, Thomas Bayes, Whole Earth Catalog

So rather than starting from scratch to build a new perception from every batch of raw data delivered by the senses, the mind jumps to the most sensible conclusion based on past experience combined with a tiny sample of that data. Our brains are prediction machines optimized by experience, and when it comes to faces, they have boatloads of experience: faces are always convex, so this hollow mask must be a prediction error to be corrected. These so-called Bayesian inferences (named for Thomas Bayes, the eighteenth-century English philosopher who developed the mathematics of probability, on which these mental predictions are based) serve us well most of the time, speeding perception while saving effort and energy, but they can also trap us in literally preconceived images of reality that are simply false, as in the case of the rotating mask.

Architects of Intelligence by Martin Ford

3D printing, agricultural Revolution, AI winter, algorithmic bias, Alignment Problem, AlphaGo, Apple II, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, backpropagation, barriers to entry, basic income, Baxter: Rethink Robotics, Bayesian statistics, Big Tech, bitcoin, Boeing 747, Boston Dynamics, business intelligence, business process, call centre, Cambridge Analytica, cloud computing, cognitive bias, Colonization of Mars, computer vision, Computing Machinery and Intelligence, correlation does not imply causation, CRISPR, crowdsourcing, DARPA: Urban Challenge, data science, deep learning, DeepMind, Demis Hassabis, deskilling, disruptive innovation, Donald Trump, Douglas Hofstadter, driverless car, Elon Musk, Erik Brynjolfsson, Ernest Rutherford, fake news, Fellow of the Royal Society, Flash crash, future of work, general purpose technology, Geoffrey Hinton, gig economy, Google X / Alphabet X, Gödel, Escher, Bach, Hans Moravec, Hans Rosling, hype cycle, ImageNet competition, income inequality, industrial research laboratory, industrial robot, information retrieval, job automation, John von Neumann, Large Hadron Collider, Law of Accelerating Returns, life extension, Loebner Prize, machine translation, Mark Zuckerberg, Mars Rover, means of production, Mitch Kapor, Mustafa Suleyman, natural language processing, new economy, Nick Bostrom, OpenAI, opioid epidemic / opioid crisis, optical character recognition, paperclip maximiser, pattern recognition, phenotype, Productivity paradox, radical life extension, Ray Kurzweil, recommendation engine, Robert Gordon, Rodney Brooks, Sam Altman, self-driving car, seminal paper, sensor fusion, sentiment analysis, Silicon Valley, smart cities, social intelligence, sparse data, speech recognition, statistical model, stealth mode startup, stem cell, Stephen Hawking, Steve Jobs, Steve Wozniak, Steven Pinker, strong AI, superintelligent machines, synthetic biology, systems thinking, Ted Kaczynski, TED Talk, The Rise and Fall of American Growth, theory of mind, Thomas Bayes, Travis Kalanick, Turing test, universal basic income, Wall-E, Watson beat the top human players on Jeopardy!, women in the workforce, working-age population, workplace surveillance , zero-sum game, Zipcar

BAYESIAN is a term that can be generally be translated as “probabilistic” or “using the rules of probability.” You may encounter terms like Bayesian machine learning or Bayesian networks; these refer to algorithms that use the rules of probability. The term derives from the name of the Reverend Thomas Bayes (1701 to 1761) who formulated a way to update the likelihood of an event based on new evidence. Bayesian methods are very popular with both computer scientists and with scientists who attempt to model human cognition. Judea Pearl, who is interviewed in this book, received the highest honor in computer science, the Turing Award, in part for his work on Bayesian techniques.

Thinking, Fast and Slow by Daniel Kahneman

Albert Einstein, Atul Gawande, availability heuristic, Bayesian statistics, behavioural economics, Black Swan, book value, Cass Sunstein, Checklist Manifesto, choice architecture, classic study, cognitive bias, cognitive load, complexity theory, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, delayed gratification, demand response, endowment effect, experimental economics, experimental subject, Exxon Valdez, feminist movement, framing effect, hedonic treadmill, hindsight bias, index card, information asymmetry, job satisfaction, John Bogle, John von Neumann, Kenneth Arrow, libertarian paternalism, Linda problem, loss aversion, medical residency, mental accounting, meta-analysis, nudge unit, pattern recognition, Paul Samuelson, peak-end rule, precautionary principle, pre–internet, price anchoring, quantitative trading / quantitative finance, random walk, Richard Thaler, risk tolerance, Robert Metcalfe, Ronald Reagan, Shai Danziger, sunk-cost fallacy, Supply of New York City Cabdrivers, systematic bias, TED Talk, The Chicago School, The Wisdom of Crowds, Thomas Bayes, transaction costs, union organizing, Walter Mischel, Yom Kippur War

And if you believe that there is a 30% chance that candidate X will be elected president, and an 80% chance that he will be reelected if he wins the first time, then you must believe that the chances that he will be elected twice in a row are 24%. The relevant “rules” for cases such as the Tom W problem are provided by Bayesian statistics. This influential modern approach to statistics is named after an English minister of the eighteenth century, the Reverend Thomas Bayes, who is credited with the first major contribution to a large problem: the logic of how people should change their mind in the light of evidence. Bayes’s rule specifies how prior beliefs (in the examples of this chapter, base rates) should be combined with the diagnosticity of the evidence, the degree to which it favors the hypothesis over the alternative.

Antifragile: Things That Gain From Disorder by Nassim Nicholas Taleb

"World Economic Forum" Davos, Air France Flight 447, Alan Greenspan, Andrei Shleifer, anti-fragile, banking crisis, Benoit Mandelbrot, Berlin Wall, biodiversity loss, Black Swan, business cycle, caloric restriction, caloric restriction, Chuck Templeton: OpenTable:, commoditize, creative destruction, credit crunch, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discrete time, double entry bookkeeping, Emanuel Derman, epigenetics, fail fast, financial engineering, financial independence, Flash crash, flying shuttle, Gary Taubes, George Santayana, Gini coefficient, Helicobacter pylori, Henri Poincaré, Higgs boson, high net worth, hygiene hypothesis, Ignaz Semmelweis: hand washing, informal economy, invention of the wheel, invisible hand, Isaac Newton, James Hargreaves, Jane Jacobs, Jim Simons, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, Kenneth Arrow, knowledge economy, language acquisition, Lao Tzu, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, Marc Andreessen, Mark Spitznagel, meta-analysis, microbiome, money market fund, moral hazard, mouse model, Myron Scholes, Norbert Wiener, pattern recognition, Paul Samuelson, placebo effect, Ponzi scheme, Post-Keynesian economics, power law, principal–agent problem, purchasing power parity, quantitative trading / quantitative finance, Ralph Nader, random walk, Ray Kurzweil, rent control, Republic of Letters, Ronald Reagan, Rory Sutherland, Rupert Read, selection bias, Silicon Valley, six sigma, spinning jenny, statistical model, Steve Jobs, Steven Pinker, Stewart Brand, stochastic process, stochastic volatility, synthetic biology, tacit knowledge, tail risk, Thales and the olive presses, Thales of Miletus, The Great Moderation, the new new thing, The Wealth of Nations by Adam Smith, Thomas Bayes, Thomas Malthus, too big to fail, transaction costs, urban planning, Vilfredo Pareto, Yogi Berra, Zipf's Law

An extraordinary proportion of work came out of the rector, the English parish priest with no worries, erudition, a large or at least comfortable house, domestic help, a reliable supply of tea and scones with clotted cream, and an abundance of free time. And, of course, optionality. The enlightened amateur, that is. The Reverends Thomas Bayes (as in Bayesian probability) and Thomas Malthus (Malthusian overpopulation) are the most famous. But there are many more surprises, cataloged in Bill Bryson’s Home, in which the author found ten times more vicars and clergymen leaving recorded traces for posterity than scientists, physicists, economists, and even inventors.

The Organized Mind: Thinking Straight in the Age of Information Overload by Daniel J. Levitin

Abraham Maslow, airport security, Albert Einstein, Amazon Mechanical Turk, Anton Chekhov, autism spectrum disorder, Bayesian statistics, behavioural economics, big-box store, business process, call centre, Claude Shannon: information theory, cloud computing, cognitive bias, cognitive load, complexity theory, computer vision, conceptual framework, correlation does not imply causation, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, data science, deep learning, delayed gratification, Donald Trump, en.wikipedia.org, epigenetics, Eratosthenes, Exxon Valdez, framing effect, friendly fire, fundamental attribution error, Golden Gate Park, Google Glasses, GPS: selective availability, haute cuisine, How many piano tuners are there in Chicago?, human-factors engineering, if you see hoof prints, think horses—not zebras, impulse control, index card, indoor plumbing, information retrieval, information security, invention of writing, iterative process, jimmy wales, job satisfaction, Kickstarter, language acquisition, Lewis Mumford, life extension, longitudinal study, meta-analysis, more computing power than Apollo, Network effects, new economy, Nicholas Carr, optical character recognition, Pareto efficiency, pattern recognition, phenotype, placebo effect, pre–internet, profit motive, randomized controlled trial, Rubik’s Cube, Salesforce, shared worldview, Sheryl Sandberg, Skype, Snapchat, social intelligence, statistical model, Steve Jobs, supply-chain management, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, traumatic brain injury, Turing test, Twitter Arab Spring, ultimatum game, Wayback Machine, zero-sum game

It’s when they’re only mildly unlikely that our brains freeze up. Organizing our decisions requires that we combine the base rate information with other relevant diagnostic information. This type of reasoning was discovered in the eighteenth century by the mathematician and Presbyterian minister Thomas Bayes, and bears his name: Bayes’s rule. Bayes’s rule allows us to refine estimates. For example, we read that roughly half of marriages end in divorce. But we can refine that estimate if we have additional information, such as the age, religion, or location of the people involved, because the 50% figure holds only for the aggregate of all people.

The Stuff of Thought: Language as a Window Into Human Nature by Steven Pinker

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The embarrassments for Hume’s two theories of causation (conjunction and counterfactuals) can be diagrammed as a family of networks in which the lines fan in or out or loop around, as in the diagram on the following page. One solution to the webbiness of causation is a technique in artificial intelligence called Causal Bayes Networks.120 (They are named for Thomas Bayes, whose eponymous theorem shows how to calculate the probability of some condition from its prior plausibility and the likelihood that it led to some observed symptoms.) A modeler chooses a set of variables (amount of coffee drunk, amount of exercise, presence of heart disease, and so on), draws arrows between causes and their effects, and labels each arrow with a number representing the strength of the causal influence (the increase or decrease in the likelihood of the effect, given the presence of the cause).

Data Mining: Concepts and Techniques: Concepts and Techniques by Jiawei Han, Micheline Kamber, Jian Pei

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This assumption is called class-conditional independence. It is made to simplify the computations involved and, in this sense, is considered “naïve." Section 8.3.1 reviews basic probability notation and Bayes’ theorem. In Section 8.3.2 you will learn how to do naïve Bayesian classification. 8.3.1. Bayes’ Theorem Bayes’ theorem is named after Thomas Bayes, a nonconformist English clergyman who did early work in probability and decision theory during the 18th century. Let X be a data tuple. In Bayesian terms, X is considered “evidence.” As usual, it is described by measurements made on a set of n attributes. Let H be some hypothesis such as that the data tuple X belongs to a specified class C.