It is not possible to add the new link because it would replace an existing, longer link.
| Line 1: | Line 1: | ||
==Basic form of model== |
==Basic form of model== |
||
The procedure for cluster-weighted modeling of an input-output problem can be outlined as follows.<ref name=nature/> In order to construct predicted values for an output variable ''y'' from an input variable ''x'', the modeling and calibration procedure arrives at a [[ |
The procedure for cluster-weighted modeling of an input-output problem can be outlined as follows.<ref name=nature/> In order to construct predicted values for an output variable ''y'' from an input variable ''x'', the modeling and calibration procedure arrives at a joint [[probability density function]], ''p''(''y'',''x''). Here the "variables" might be uni-variate, multivariate or time-series. For convenience, any model parameters are not indicated in the notation here and several different treatments of these are possible, including setting them to fixed values as a step in the calibration or treating them using a [[Bayesian analysis]]. The required predicted values are obtained by constructing the [[conditional probability distribution|conditional probability density]] ''p''(''y''|''x'') from which the prediction using the [[conditional expected value]] can be obtained, with the [[conditional variance]] providing an indication of uncertainty. |
||
The important step of the modeling is that ''p''(''y''|''x'') is assumed to take the following form, as a [[mixture model]]: |
The important step of the modeling is that ''p''(''y''|''x'') is assumed to take the following form, as a [[mixture model]]: |
||