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Abstract:
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Two aspects of predictive analysis will be considered: choosing a regression equation for prediction and predictive distributions for future observations. Articles from 1920 and the 1960s will be discussed as precursors to modern "predictive analytics" for such problems. In 1960, Nicholson expounded upon the fact of "shrinkage" in regression, as happens when a predicting function developed on training data is applied to future observations. Also in 1960, Stein considered this problem and developed a criterion for choosing a regression equation for prediction, with an adjustment reminiscent of that in adjusted R-square. Consider the problem of modeling a data set of employee days ill, or accidents in a population of insureds. One can consider a spectrum of granularity in describing the population, from a single distribution to a bimodal distribution to a mixture of two or more distributions, where there are two or more subpopulations, to modeling the population at the individual level, where each individual in a way constitutes a subpopulation. Cluster analysis, the mixture model, and Bayesian models will be considered as one moves across this spectrum.
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