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Bayesian analysis of the patterns of biological susceptibility via reversible jump MCMC sampling

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  • Liu, Rui-Yin
  • Tao, Jian
  • Shi, Ning-Zhong
  • He, Xuming

Abstract

In some biological experiments, it is quite common that laboratory subjects differ in their patterns of susceptibility to a treatment. Finite mixture models are useful in those situations. In this paper we model the number of components and the component parameters jointly, and base inference about these quantities on their posterior probabilities, making use of the reversible jump Markov chain Monte Carlo methods. In particular, we apply the methodology to the analysis of univariate normal mixtures with multidimensional parameters, using a hierarchical prior model that allows weak priors while avoiding improper priors in the mixture context. The practical significance of the proposed method is illustrated with a dose-response data set.

Suggested Citation

  • Liu, Rui-Yin & Tao, Jian & Shi, Ning-Zhong & He, Xuming, 2011. "Bayesian analysis of the patterns of biological susceptibility via reversible jump MCMC sampling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1498-1508, March.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1498-1508
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    References listed on IDEAS

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    1. Kenny S. Crump, 1995. "Calculation of Benchmark Doses from Continuous Data," Risk Analysis, John Wiley & Sons, vol. 15(1), pages 79-89, February.
    2. Tao, Jian & Shi, Ning-Zhong & Lee, S.-Y.Sik-Yum, 2004. "Drug risk assessment with determining the number of sub-populations under finite mixture normal models," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 661-676, July.
    3. 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.
    4. Mehdi Razzaghi & Ralph L. Kodell, 2000. "Risk Assessment for Quantitative Responses Using a Mixture Model," Biometrics, The International Biometric Society, vol. 56(2), pages 519-527, June.
    5. Ralph L. Kodell & Ronnie W. West, 1993. "Upper Confidence Limits on Excess Risk for Quantitative Responses," Risk Analysis, John Wiley & Sons, vol. 13(2), pages 177-182, April.
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    Cited by:

    1. 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.
    2. Drovandi, Christopher C. & Pettitt, Anthony N. & Henderson, Robert D. & McCombe, Pamela A., 2014. "Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 128-146.

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