A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihoods

David Ardia, Nalan Basturk, Lennart Hoogerheide & Herman Van Dijk

Résumé 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.
Mots-clés Marginal likelihood; Bayes factor; Importance sampling; Bridge sampling; Adaptive mixture of Student-tt distributions
Citation Ardia, D., Basturk, N., Hoogerheide, L., & Van Dijk , H. (2012). A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihoods. Computational Statistics & Data Analysis, 56(11), 3398-3414.
Type Article de périodique (Anglais)
Date de publication 2012
Nom du périodique Computational Statistics & Data Analysis
Volume 56
Numéro 11
Pages 3398-3414
URL http://www.sciencedirect.com/science/article/pii/S0167947...
Liée au projet Bayesian estimation of regime-switching GARCH models