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A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood

David Ardia, Nalan Baştürk, Lennart Hoogerheide and Herman van Dijk

Computational Statistics & Data Analysis, 2012, vol. 56, issue 11, 3398-3414

Abstract: Strategic choices for efficient and accurate evaluation of marginal likelihoods by means of Monte Carlo simulation methods are studied for the case of highly non-elliptical posterior distributions. A comparative analysis is presented of possible advantages and limitations of different simulation techniques; of possible choices of candidate distributions and choices of target or warped target distributions; and finally of numerical standard errors. The importance of a robust and flexible estimation strategy is demonstrated where the complete posterior distribution is explored. Given an appropriately yet quickly tuned adaptive candidate, straightforward importance sampling provides a computationally efficient estimator of the marginal likelihood (and a reliable and easily computed corresponding numerical standard error) in the cases investigated, which include a non-linear regression model and a mixture GARCH model. Warping the posterior density can lead to a further gain in efficiency, but it is more important that the posterior kernel be appropriately wrapped by the candidate distribution than that it is warped.

Keywords: Marginal likelihood; Bayes factor; Importance sampling; Bridge sampling; Adaptive mixture of Student-t distributions (search for similar items in EconPapers)
Date: 2012
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Working Paper: A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood (2010) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:11:p:3398-3414

DOI: 10.1016/j.csda.2010.09.001

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