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

Tomohiro Ando

Research output: Contribution to journalArticle

115 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

Fingerprint

Posterior Mean
Empirical Bayes
Information Criterion
Predictive Distribution
Estimator
Evaluation
Hierarchical Bayesian Model
Model Evaluation
Asymptotic Bias
Bias Correction
probability distribution
Random Effects
Bootstrap
Probability distributions
Probability Distribution
Model
Information criterion
Predictive distribution

Keywords

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

ASJC Scopus subject areas

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

Cite this

Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models. / Ando, Tomohiro.

In: Biometrika, Vol. 94, No. 2, 06.2007, p. 443-458.

Research output: Contribution to journalArticle

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