# 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)

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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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