Marginal likelihood estimation via power posteriors
Model choice plays an increasingly important role in statistics. From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model. However, this is typically a difficult task since it amounts to integrating over all model parameters. The aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling. We show how the marginal likelihood can be computed via Markov chain Monte Carlo methods on modified posterior distributions for each model. This then allows Bayes factors or posterior model probabilities to be calculated. We show that this approach requires very little tuning and is straightforward to implement. The new method is illustrated in a variety of challenging statistical settings. Copyright (c) 2008 Royal Statistical Society.
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Volume (Year): 70 (2008)
Issue (Month): 3 ()
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- R. Reeves, 2004. "Efficient recursions for general factorisable models," Biometrika, Biometrika Trust, vol. 91(3), pages 751-757, September.
- Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
- S. P. Brooks & P. Giudici & G. O. Roberts, 2003. "Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 3-39.
- 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.
- Sisson, Scott A., 2005. "Transdimensional Markov Chains: A Decade of Progress and Future Perspectives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1077-1089, September.
- P. G. Ridall & A. N. Pettitt & N. Friel & P. A. McCombe & R. D. Henderson, 2007. "Motor unit number estimation using reversible jump Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(3), pages 235-269.
- Ian L. Dryden & Mark R. Scarr & Charles C. Taylor, 2003. "Bayesian texture segmentation of weed and crop images using reversible jump Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 31-50.
- Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
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