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Reversible Jump MCMC in mixtures of normal distributions with the same component means

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  • Papastamoulis, Panagiotis
  • Iliopoulos, George

Abstract

The Bayesian estimation of a special case of mixtures of normal distributions with an unknown number of components is considered. More specifically, the case where some components may have identical means is studied. The standard Reversible Jump MCMC algorithm for the estimation of a normal mixture model consisting of components with distinct parameters naturally fails to give precise results in the case where (at least) two of the mixture components have equal means. In particular, this algorithm either tends to combine such components resulting in a posterior distribution for their number having mode at a model with fewer components than those of the true one, or overestimates the number of components. This problem is overcome by defining-for every number of components-models with different number of parameters and introducing a new move type that bridges these competing models. The proposed method is applied in conjunction with suitable modifications of the standard split-combine and birth-death moves for updating the number of components. The method is illustrated by using two simulated datasets and the well-known galaxy dataset.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:900-911
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    References listed on IDEAS

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    1. 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.
    2. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    3. Garel, Bernard, 2007. "Recent asymptotic results in testing for mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5295-5304, July.
    4. repec:dau:papers:123456789/1906 is not listed on IDEAS
    5. repec:dau:papers:123456789/6069 is not listed on IDEAS
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    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. Papastamoulis Panagiotis & Rattray Magnus, 2017. "Bayesian estimation of differential transcript usage from RNA-seq data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(5-6), pages 387-405, December.
    3. Kazuhiko Kakamu, 2022. "Bayesian analysis of mixtures of lognormal distribution with an unknown number of components from grouped data," Papers 2210.05115, arXiv.org, revised Sep 2023.
    4. Liu, Hefei & Song, Xinyuan, 2021. "Bayesian analysis of hidden Markov structural equation models with an unknown number of hidden states," Econometrics and Statistics, Elsevier, vol. 18(C), pages 29-43.
    5. Papastamoulis, Panagiotis, 2018. "Overfitting Bayesian mixtures of factor analyzers with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 220-234.
    6. Papastamoulis, Panagiotis, 2016. "label.switching: An R Package for Dealing with the Label Switching Problem in MCMC Outputs," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(c01).

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