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 language | English |
|---|---|
| Pages (from-to) | 443-458 |
| Number of pages | 16 |
| Journal | Biometrika |
| Volume | 94 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2007 Jun |
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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 journal › Article
}
TY - JOUR
T1 - Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models
AU - Ando, Tomohiro
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
UR - http://www.scopus.com/inward/record.url?scp=34548388929&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34548388929&partnerID=8YFLogxK
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 -