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Computing marginal likelihoods from a single MCMC output

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  • Ming‐Hui Chen

Abstract

In this article, we propose new Monte Carlo methods for computing a single marginal likelihood or several marginal likelihoods for the purpose of Bayesian model comparisons. The methods are motivated by Bayesian variable selection, in which the marginal likelihoods for all subset variable models are required to compute. The proposed estimates use only a single Markov chain Monte Carlo (MCMC) output from the joint posterior distribution and it does not require the specific structure or the form of the MCMC sampling algorithm that is used to generate the MCMC sample to be known. The theoretical properties of the proposed method are examined in detail. The applicability and usefulness of the proposed method are demonstrated via ordinal data probit regression models. A real dataset involving ordinal outcomes is used to further illustrate the proposed methodology.

Suggested Citation

  • Ming‐Hui Chen, 2005. "Computing marginal likelihoods from a single MCMC output," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 16-29, February.
    • Handle: RePEc:bla:stanee:v:59:y:2005:i:1:p:16-29
    DOI: 10.1111/j.1467-9574.2005.00276.x
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    Cited by:

    1. Perrakis, Konstantinos & Ntzoufras, Ioannis & Tsionas, Efthymios G., 2014. "On the use of marginal posteriors in marginal likelihood estimation via importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 54-69.
    2. Jonathan W Armond & Edward F Harry & Andrew D McAinsh & Nigel J Burroughs, 2015. "Inferring the Forces Controlling Metaphase Kinetochore Oscillations by Reverse Engineering System Dynamics," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-26, November.
    3. Tian, Guo-Liang & Ng, Kai Wang & Li, Kai-Can & Tan, Ming, 2009. "Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3314-3323, July.
    4. Kim, Hea-Jung, 2018. "Bayesian hierarchical robust factor analysis models for partially observed sample-selection data," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 65-82.
    5. Ehlers, Ricardo S., 2012. "Computational tools for comparing asymmetric GARCH models via Bayes factors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 858-867.

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