Desiderata for a predictive theory of statistics

Abstract

In many contexts the predictive validation of models or their associated prediction strategies is of greater importance than model identification which may be practically impossible. This is particularly so in fields involving complex or high dimensional data where model selection, or more generally predictor selection is the main focus of effort. This paper suggests a unified treatment for predictive analyses based on six `desiderata'. These desiderata are an effort to clarify what criteria a good predictive theory of statistics should satisfy.