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A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood

Author

Listed:
  • David Ardia

    (University of Fribourg, aeris CAPITAL AG, Switzerland)

  • Nalan Basturk

    (Erasmus University Rotterdam)

  • Lennart Hoogerheide

    (Erasmus University Rotterdam)

  • Herman K. van Dijk

    (Erasmus University Rotterdam)

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.

Suggested Citation

  • David Ardia & Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2010. "A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood," Tinbergen Institute Discussion Papers 10-059/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20100059
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    References listed on IDEAS

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    4. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
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    23. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
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    More about this item

    Keywords

    marginal likelihood; Bayes factor; importance sampling; bridge sampling; adaptive mixture of Student-t distributions;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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