To Bridge, to Warp or to Wrap? A Comperative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood

Computational Statistics & Data Analysis, Vol. 56, No. 11, pp. 3398-3414, 2012

TI Discussion Paper No. 09-017/4

44 Pages Posted: 26 Feb 2009 Last revised: 13 May 2015

See all articles by David Ardia

David Ardia

HEC Montreal - Department of Decision Sciences

Lennart F. Hoogerheide

VU University Amsterdam

H. K. van Dijk

Tinbergen Institute; Econometric Institute

Date Written: February 26, 2009

Abstract

Important 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. We focus on the situation where one makes use of importance sampling or the independence chain Metropolis-Hastings algorithm for posterior analysis. 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. In this respect, the adaptive mixture of Student-t distributions of Hoogerheide et al.(2007) works particularly well. Given an appropriately yet quickly tuned candidate, straightforward importance sampling provides the most efficient estimator of the marginal likelihood in the cases investigated in this paper, which include a non-linear regression model of Ritter and Tanner (1992) and a conditional normal distribution of Gelman and Meng (1991). A poor choice of candidate density may lead to a huge loss of efficiency where the numerical standard error may be highly unreliable.

Keywords: marginal likelihood, Bayes factor, importance sampling, Markov chain Monte Carlo, bridge sampling, adaptive mixture of Student-t distributions

JEL Classification: C11, C15, C52

Suggested Citation

Ardia, David and Hoogerheide, Lennart F. and van Dijk, Herman K., To Bridge, to Warp or to Wrap? A Comperative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood (February 26, 2009). Computational Statistics & Data Analysis, Vol. 56, No. 11, pp. 3398-3414, 2012, TI Discussion Paper No. 09-017/4, Available at SSRN: https://ssrn.com/abstract=1349876

David Ardia

HEC Montreal - Department of Decision Sciences ( email )

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Lennart F. Hoogerheide (Contact Author)

VU University Amsterdam ( email )

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Herman K. Van Dijk

Tinbergen Institute ( email )

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Econometric Institute ( email )

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