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.

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Tinbergen Institute
Tinbergen Institute Discussion Paper Series
Discussion paper / Tinbergen Institute
Tinbergen Institute

David, D, Basturk, N, Hoogerheide, L.F, & van Dijk, H.K. (2010). A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihoods (No. TI 2010-059/4). Discussion paper / Tinbergen Institute (pp. 1–33). Tinbergen Institute. Retrieved from