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Efficient Bayes factor estimation from the reversible jump output

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  • Francesco Bartolucci
  • Luisa Scaccia
  • Antonietta Mira

Abstract

We propose a class of estimators of the Bayes factor which is based on an extension of the bridge sampling identity of Meng & Wong (1996) and makes use of the output of the reversible jump algorithm of Green (1995). Within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models. The proposed estimators are very easily computed and lead to a substantial gain of efficiency in estimating the Bayes factor over the standard estimator based on the reversible jump output. This is illustrated through a series of Monte Carlo simulations involving a linear and a logistic regression model. Copyright 2006, Oxford University Press.

Suggested Citation

  • Francesco Bartolucci & Luisa Scaccia & Antonietta Mira, 2006. "Efficient Bayes factor estimation from the reversible jump output," Biometrika, Biometrika Trust, vol. 93(1), pages 41-52, March.
  • Handle: RePEc:oup:biomet:v:93:y:2006:i:1:p:41-52
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    File URL: http://hdl.handle.net/10.1093/biomet/93.1.41
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    Cited by:

    1. Rufo, M.J. & Martín, J. & Pérez, C.J., 2010. "New approaches to compute Bayes factor in finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3324-3335, December.
    2. David I. Hastie & Peter J. Green, 2012. "Model choice using reversible jump Markov chain Monte Carlo," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 309-338, August.
    3. Pandolfi, Silvia & Bartolucci, Francesco & Friel, Nial, 2014. "A generalized multiple-try version of the Reversible Jump algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 298-314.
    4. Shotwell Matthew S & Slate Elizabeth H, 2010. "Bayesian Modeling of Footrace Finishing Times," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(3), pages 1-21, July.
    5. N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607.
    6. repec:dau:papers:123456789/5724 is not listed on IDEAS
    7. Nicolas Chopin & Christian P. Robert, 2010. "Properties of nested sampling," Biometrika, Biometrika Trust, vol. 97(3), pages 741-755.

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