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

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  • Tomohiro Ando

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. Copyright 2007, Oxford University Press.

Suggested Citation

  • Tomohiro Ando, 2007. "Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models," Biometrika, Biometrika Trust, vol. 94(2), pages 443-458.
  • Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:443-458
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    File URL: http://hdl.handle.net/10.1093/biomet/asm017
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    Cited by:

    1. Ando, Tomohiro, 2009. "Bayesian portfolio selection using a multifactor model," International Journal of Forecasting, Elsevier, vol. 25(3), pages 550-566, July.
    2. Abanto-Valle, C.A. & Bandyopadhyay, D. & Lachos, V.H. & Enriquez, I., 2010. "Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2883-2898, December.
    3. José L. Gallizo & Jordi Moreno & Manuel Salvador, 2016. "Banking Efficiency in the Enlarged European Union: Financial Crisis and Convergence," International Finance, Wiley Blackwell, vol. 19(1), pages 66-88, April.
    4. repec:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-016-9530-0 is not listed on IDEAS
    5. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
    6. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2015. "A Variant of AIC Using Bayesian Marginal Likelihood," CIRJE F-Series CIRJE-F-971, CIRJE, Faculty of Economics, University of Tokyo.
    7. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    8. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
    9. Tomohiro Ando, 2012. "Bayesian portfolio selection under a multifactor asset return model with predictive model selection," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 14(1/2), pages 77-101.
    10. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, vol. 26(2), pages 413-434, April.
    11. Ando, Tomohiro, 2009. "Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1717-1726, September.
    12. Wang, Yixin & So, Mike K.P., 2016. "A Bayesian hierarchical model for spatial extremes with multiple durations," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 39-56.
    13. repec:bla:biomet:v:73:y:2017:i:1:p:52-62 is not listed on IDEAS
    14. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    15. Ando, Tomohiro, 2009. "Bayesian inference for the hazard term structure with functional predictors using Bayesian predictive information criteria," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1925-1939, April.
    16. Nandram Balgobin, 2016. "Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model," Journal of Official Statistics, Sciendo, vol. 32(1), pages 187-208, March.
    17. Ando, Tomohiro & Tsay, Ruey, 2010. "Predictive likelihood for Bayesian model selection and averaging," International Journal of Forecasting, Elsevier, vol. 26(4), pages 744-763, October.
    18. repec:spr:sankhb:v:80:y:2018:i:1:d:10.1007_s13571-018-0152-7 is not listed on IDEAS
    19. Liang Yulan & Kelemen Arpad, 2016. "Bayesian state space models for dynamic genetic network construction across multiple tissues," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(4), pages 273-290, August.

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