Abstract: Empirical Bayes modeling has a long and celebrated history in statistical theory and applications. After a brief review of the literature, we propose a new dynamic empirical Bayes modeling approach that provides flexible and computationally efficient methods for the analysis and prediction of longitudinal data from many individuals. This 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 approach to modeling default probabilities of firms that are jointly exposed to some unobservable dynamic risk factor, and to the well-known statistical problem of predicting baseball batting averages studied by Efron and Morris and recently by Brown.

Key words and phrases: Dynamic frailty model, empirical Bayes, generalized linear mixed models, longitudinal data, prediction, time series.