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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 K. van Dijk
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Lennart Hoogerheide: Erasmus University Rotterdam

No 10-059/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper resulted in an article in Computational Statistics & Data Analysis (2012). Vol. 56(11), 3398-3414.

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 in this paper, 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 is appropriately wrapped by the candidate distribution than that is warped.

Keywords: marginal likelihood; Bayes factor; importance sampling; bridge sampling; adaptive mixture of Student-t distributions (search for similar items in EconPapers)
JEL-codes: C11 C15 C52 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2010-06-21
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