2007/02/28 by Tomohiro Ando · 251 citations
Mathematics · #Statistical Methods and Inference #Statistical Methods and Bayesian Inference #Advanced Statistical Methods and Models #Bayes' theorem #Bayesian probability #Mathematics #Bayes factor #Bayesian programming #Bayesian hierarchical modeling #Naive Bayes classifier #Bayesian statistics #Machine learning #Econometrics #Bayesian linear regression #Bayesian inference #Artificial intelligence #Statistics #Computer science #Support vector machine
paper · doi:10.1093/biomet/asm017
published in Biometrika 94(2), 443-458 (Oxford University Press)
openalex publication_date 2007/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/27
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.