Publications [#257653] of James O. Berger
Papers Published
- Scott, JG; Berger, JO. "Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem." The Annals of Statistics 38.5 (October, 2010): 2587-2619. [repository], [doi]
(last updated on 2024/01/01)Abstract:
This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.