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New approaches to compute Bayes factor in finite mixture models

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  • Rufo, M.J.
  • Martín, J.
  • Pérez, C.J.
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    Abstract

    Two new approaches to estimate Bayes factors in a finite mixture model context are proposed. Specifically, two algorithms to estimate them and their errors are derived by decomposing the resulting marginal densities. Then, through Bayes factor comparisons, the appropriate number of components for the mixture model is obtained. The approaches are based on simple theory (Monte Carlo methods and cluster sampling), what makes them appealing tools in this context. The performance of both algorithms is studied for different situations and the procedures are illustrated with some previously published data sets.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 12 (December)
    Pages: 3324-3335

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3324-3335

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Bayes factor Cluster sampling Conjugate prior distribution Finite mixture model Marginal distribution Monte Carlo methods;

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    1. Siddhartha Chib & Ivan Jeliazkov, 2005. "Accept-reject Metropolis-Hastings sampling and marginal likelihood estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 30-44.
    2. Cappé, Olivier & Robert, Christian P. & Ryden, Tobias, 2003. "Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers," Economics Papers from University Paris Dauphine 123456789/6040, Paris Dauphine University.
    3. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, 06.
    4. Congdon, Peter, 2006. "Bayesian model choice based on Monte Carlo estimates of posterior model probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 346-357, January.
    5. Olivier Cappé & Christian P. Robert & Tobias Rydén, 2003. "Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 679-700.
    6. Bohning, Dankmar & Seidel, Wilfried, 2003. "Editorial: recent developments in mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 349-357, January.
    7. Papastamoulis, Panagiotis & Iliopoulos, George, 2009. "Reversible Jump MCMC in mixtures of normal distributions with the same component means," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 900-911, February.
    8. 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.
    9. Robert, Christian P. & Marin, Jean-Michel, 2008. "Approximating the marginal likelihood in mixture models," Economics Papers from University Paris Dauphine 123456789/3692, Paris Dauphine University.
    10. Song, Xin-Yuan & Lee, Sik-Yum, 2002. "A Bayesian model selection method with applications," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 539-557, September.
    11. M. Rufo & J. Martín & C. Pérez, 2006. "Bayesian analysis of finite mixture models of distributions from exponential families," Computational Statistics, Springer, vol. 21(3), pages 621-637, December.
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