Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models

Tomohiro Ando

Research output: Contribution to journalArticle

122 Citations (Scopus)

Abstract

The problem of evaluating the goodness of the predictive distributions of hierarchical Bayesian and empirical Bayes models is investigated. A Bayesian predictive information criterion is proposed as an estimator of the posterior mean of the expected loglikelihood of the predictive distribution when the specified family of probability distributions does not contain the true distribution. The proposed criterion is developed by correcting the asymptotic bias of the posterior mean of the loglikelihood as an estimator of its expected loglikelihood. In the evaluation of hierarchical Bayesian models with random effects, regardless of our parametric focus, the proposed criterion considers the bias correction of the posterior mean of the marginal loglikelihood because it requires a consistent parameter estimator. The use of the bootstrap in model evaluation is also discussed.

Original languageEnglish
Pages (from-to)443-458
Number of pages16
JournalBiometrika
Volume94
Issue number2
DOIs
Publication statusPublished - 2007 Jun 1

Keywords

  • Empirical Bayes model
  • Hierarchical Bayesian model
  • Markov chain Monte Carlo
  • Model misspecification

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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