Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2010-06-21 Number: 10-059/4 Author-Name: David Ardia Author-Workplace-Name: University of Fribourg, aeris CAPITAL AG, Switzerland Author-Name: Nalan Basturk Author-Workplace-Name: Erasmus University Rotterdam Author-Name: Lennart Hoogerheide Author-Workplace-Name: Erasmus University Rotterdam Author-Name: Herman K. van Dijk Author-Workplace-Name: Erasmus University Rotterdam Title: A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood Abstract: This discussion paper resulted in an article in Computational Statistics & Data Analysis, 2012, 56(11), 3398-3414.
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. Classification-JEL: C11, C15, C52 Keywords: marginal likelihood, Bayes factor, importance sampling, bridge sampling, adaptive mixture of Student-t distributions File-Url: http://papers.tinbergen.nl/10059.pdf File-Format: application/pdf File-Size: 1771064 bytes Handle: RePEc:tin:wpaper:20100059