Dynamic empirical Bayes models and their applications to longitudinal data analysis and prediction

Abstract

Empirical Bayes modeling has a long and celebrated history in statistical theory and applications. In particular, in insurance rate-making, linear empirical Bayes models have provided a basic framework for credibility theory. However, evolutionary credibility models, in which the individual risk profiles evolve over time, have not used the empirical Bayes framework but have relied on minimum-variance linear estimation via Kalman filtering. After a brief review of the literature, we propose a new dynamic empirical Bayes modeling approach which provides flexible and computationally efficient methods for the analysis and prediction of longitudinal data from many individuals. This dynamic empirical Bayes approach pools the cross-sectional information over individual time series to replace an inherently complicated hidden Markov model by a considerably simpler generalized linear mixed model. We apply this new approach to evolutionary credibility theory and to the well-known statistical problem of predicting baseball batting averages studied by Efron and Morris and recently by Brown.