Abstract #300945

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JSM 2003 Abstract #300945
Activity Number: 366
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300945
Title: Bayesian Cross-Validation: A Comparison of Estimators
Author(s): Kristin A. Duncan*+ and Steven N. MacEachern
Companies: The Ohio State University and Ohio State University
Address: 2002 W Schantz Ave., Kettering, OH, 45409-2129,
Keywords: cross-validation ; Bayesian analysis ; model assessment
Abstract:

Cross-validation is routinely used to assess models. We examine cross-validation in Bayesian analysis. Three versions of cross-validation are compared; full (leave one out), poor man's (leave none out), and covariate included. In covariate included cross-validation, we leave out one value of the response variable when fitting the model while including the covariates for this observation in the computation of the posterior distribution. We show that in Bayesian analysis the poor man's cross-validation estimator can sometimes result in a larger estimated discrepancy than the full cross-validation estimator. We consider the effect of one additional observation on the discrepancy and give conditions under which the poor man's cross-validation estimator yields a smaller estimated discrepancy than the full cross-validation estimator. We also examine covariate included cross-validation for a normal linear regression model and demonstrate when this covariate included cross-validation estimator will differ from the full cross-validation estimator.

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