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.

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Keywords Adaptive mixture of Student-t distributions, Bayes factor, Bridge sampling, Importance sampling, Marginal likelihood
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Journal Computational Statistics & Data Analysis
Note Article in press - dd November 2010
David, D, Hoogerheide, L.F, & van Dijk, H.K. (2012). A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood. Computational Statistics & Data Analysis, 56(11), 3398–3414. doi:10.1016/j.csda.2010.09.001