Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
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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.
Published Version (Please cite this version)10.1214/10-AOS792
Publication InfoBerger, JO; & Scott, James G (2010). Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem. Annals of Statistics, 38(5). pp. 2587-2619. 10.1214/10-AOS792. Retrieved from http://hdl.handle.net/10161/4408.
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