The Need for More Emphasis on Prediction: A "Nondenominational" Model-Based Approach

Prediction problems are ubiquitous. In a model-based approach to predictive inference, the values of random variables that are presently observable are used to make inferences about the values of random variables that will become observable in the future, and the joint distribution of the random variables or various of its characteristics are assumed to be known up to the value of a vector of unknown parameters. Such an approach has proved to be highly effective in many important applications.This article argues that the performance of a prediction procedure in repeated application is important and should play a significant role in its evaluation. A "nondenominational" model-based approach to predictive inference is described and discussed; what in a Bayesian approach would be regarded as a prior distribution is simply regarded as part of a model that is hierarchical in nature. Some specifics are given for mixed-effects linear models, and an application to the prediction of the outcomes of basketball or football games (and to the ranking and rating of basketball or football teams) is included for purposes of illustration.