Empirical Bayes Estimates for Large-Scale Prediction Problems.

Classical prediction methods such as Fisher's linear discriminant function were designed for small-scale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10,000 genes, each of which is a potential predictor. This paper proposes an empirical Bayes approach to large-scale prediction, where the optimum Bayes prediction rule is estimated employing the data from all the predictors. Microarray examples are used to illustrate the method. The results show a close connection with the shrunken centroids algorithm of Tibshirani et al. (2002), a frequentist regularization approach to large-scale prediction, and also with false discovery rate theory.