TY - JOUR
T1 - Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models
AU - Ando, Tomohiro
N1 - Funding Information:
ACKNOWLEDGEMENT The author would like to thank Professor A. E. Gelfand and Dr. D. J. Spiegelhalter for constructive and helpful comments. The author is grateful to Professor S. Konishi for his comments and advices. The author gratefully acknowledges the constructive suggestions of the editor, the associate editor and two anonymous referees, which have greatly improved the paper. The author is also grateful to them for pointing out several references. This study was supported in part by a Grant-in-Aid for Young Scientists.
PY - 2007/6
Y1 - 2007/6
N2 - 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.
AB - 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.
KW - Empirical Bayes model
KW - Hierarchical Bayesian model
KW - Markov chain Monte Carlo
KW - Model misspecification
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U2 - 10.1093/biomet/asm017
DO - 10.1093/biomet/asm017
M3 - Article
AN - SCOPUS:34548388929
VL - 94
SP - 443
EP - 458
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 2
ER -