Empirical Bayes

Roger Koenker is an Honorary Professor of Economics at University College London. He was a member of the technical staff of Bell Labs and Professor of Economics and Statistics at the University of Illinois. He is a fellow of the Econometric Society, the ASA and the IMS. Jiaying Gu is an Associate Professor of Economics at the University of Toronto.

'For over a century, most statisticians have known that, in parametric inference problems, Bayes's theorem provides the best achievable informational summary of the data if certain prior information was available. For nearly that long, some statisticians have sought to extract sufficient information from the same data to provide a reasonable substitute for the needed prior information, in effect allowing the analyst to reach near perfection without making unreasonable prior assumptions. Koenker and Gu summarize and advance this program with a welcome display of what may be termed these days 'Natural Intelligence.' Stephen M. Stigler, University of Chicago

• 1. Introduction; 2. The empirical bayes paradigm; 3. Parametric empirical bayes methods; 4. Nonparametric empirical bayes methods; 5. Mixture models; 6. Heteroscedastic gaussian mixture models and longitudinal data; 7. Ranking and selection as compound decisions; 8. Empirical bayes methods for survival analysis; 9. Mixture models for categorical data; 10. Random coefficient models; 11. Inference for empirical bayes procedures; 12. Computational considerations; 13. Conclusion; Bibliography; Subject Index; Names Index.