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Improved Marginal Likelihood Estimation via Power Posteriors and Importance Sampling

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  • Li, Yong

    (Renmin University of China)

  • Wang, Nianling

    (Renmin University of China)

  • Yu, Jun

    (School of Economics, Singapore Management University)

Abstract

The power-posterior method of Friel and Pettitt (2008) has been used to estimate the marginal likelihoods of competing Bayesian models. In this paper it is shown that the Bernstein-von Mises (BvM) theorem holds for the power posteriors under regularity conditions. Due to the BvM theorem, the power posteriors, when adjusted by the square root of the corresponding grid points, converge to the same normal distribution as the original posterior distribution, facilitating the implementation of importance sampling for the purpose of estimating the marginal likelihood. Unlike the power-posterior method that requires repeated posterior sampling from the power posteriors, the new method only requires the posterior output from the original posterior. Hence, it is computationally more efficient to implement. Moreover, it completely avoids the coding efforts associated with drawing samples from the power posteriors. Numerical efficiency of the proposed method is illustrated using two models in economics and finance.

Suggested Citation

  • Li, Yong & Wang, Nianling & Yu, Jun, 2019. "Improved Marginal Likelihood Estimation via Power Posteriors and Importance Sampling," Economics and Statistics Working Papers 16-2019, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2019_016
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    References listed on IDEAS

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    1. Han C. & Carlin B. P., 2001. "Markov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1122-1132, September.
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    5. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    6. Li, Yong & Yu, Jun & Zeng, Tao, 2020. "Deviance information criterion for latent variable models and misspecified models," Journal of Econometrics, Elsevier, vol. 216(2), pages 450-493.
    7. Young, Karen D. S. & Pettit, Lawrence I., 1996. "On priors and Bayes factors," Journal of Econometrics, Elsevier, vol. 75(1), pages 113-119, November.
    8. N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607, July.
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    Cited by:

    1. Liu, Xiaobin & Li, Yong & Yu, Jun & Zeng, Tao, 2022. "Posterior-based Wald-type statistics for hypothesis testing," Journal of Econometrics, Elsevier, vol. 230(1), pages 83-113.

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    More about this item

    Keywords

    Bayes factor; Marginal likelihood; Markov Chain Monte Carlo; Model choice; Power posteriors; Importance sampling;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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