Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem

Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem

James G. Scott and James O. Berger

Duke University

April 2008

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. The first goal of the paper is to clarify when, and how, multiplicity correction is automatic in Bayesian analysis, and contrast this multiplicity correction with the Bayesian Ockham's-razor effect. Secondly, we contrast empirical-Bayes and fully Bayesian approaches to variable selection, through examples, theoretical results, and simulations. Considerable differences between the results of the two approaches are found, which suggest that considerable care be taken with the empirical-Bayes approach in variable selection.

Keywords: linear regression; empirical Bayes; multiple testing; Bayesian model selection


The manuscript is in available in PDF format.


Cite as:

@TechReport{Scott:Berger2008,
      Author = "James G.~Scott and James O.~Berger",
       Title = "Bayes and Empirical-{B}ayes Multiplicity Adjustment in the Variable-Selection Problem", 
        Year = 2008,
 Institution = "Duke University Department of Statistical Science",
        Type = "Discussion Paper",
      Number = "2008-10",
}