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.

Additional Metadata
Keywords Bayes factor, adaptive mixture of Student-t distributions, bridge sampling, importance sampling, marginal likelihood
Publisher Tinbergen Institute
Persistent URL hdl.handle.net/1765/19830
Citation
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 http://hdl.handle.net/1765/19830