On the calibration of Bayesian model choice criteria


Journal Article

Model choice is a fundamental problem in data analysis. With interest in hierarchical models which typically arise as Bayesian specifications, we confine ourselves to Bayesian model choice criteria. If Y denotes the observed data and T(Y) is the criterion, our goal is to calibrate T(Y) in order to assess how large or small it is under a given model. In particular, if we have the distribution of T(Y), then we can compute any probabilities or determine any quantities of interest. Apart from very special cases, analytic development of such distributions is intractable. Standard analytic approximations may be inapplicable if usual random effects are introduced at the various modeling levels. Indeed, calculation of T(Y) itself is often difficult enough. We suggest a generic simulation-intensive approach for obtaining the distribution of T(Y) to arbitrary accuracy. We focus on various Bayes factors, e.g., the usual Bayes factor, the posterior Bayes factor and the pseudo-Bayes factor. We illustrate with a binomial regression example. © 2002 Elsevier Science B.V. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Vlachos, PK; Gelfand, AE

Published Date

  • February 1, 2003

Published In

Volume / Issue

  • 111 / 1-2

Start / End Page

  • 223 - 234

International Standard Serial Number (ISSN)

  • 0378-3758

Digital Object Identifier (DOI)

  • 10.1016/S0378-3758(02)00304-X

Citation Source

  • Scopus