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Gibbs ensembles for nearly compatible and incompatible conditional models

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  • Chen, Shyh-Huei
  • Ip, Edward H.
  • Wang, Yuchung J.

Abstract

The Gibbs sampler has been used exclusively for compatible conditionals that converge to a unique invariant joint distribution. However, conditional models are not always compatible. In this paper, a Gibbs sampling-based approach-using the Gibbs ensemble-is proposed for searching for a joint distribution that deviates least from a prescribed set of conditional distributions. The algorithm can be easily scalable, such that it can handle large data sets of high dimensionality. Using simulated data, we show that the proposed approach provides joint distributions that are less discrepant from the incompatible conditionals than those obtained by other methods discussed in the literature. The ensemble approach is also applied to a data set relating to geno-polymorphism and response to chemotherapy for patients with metastatic colorectal cancer.

Suggested Citation

  • Chen, Shyh-Huei & Ip, Edward H. & Wang, Yuchung J., 2011. "Gibbs ensembles for nearly compatible and incompatible conditional models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1760-1769, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1760-1769
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    References listed on IDEAS

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    1. Barry Arnold & D. Gokhale, 1998. "Distributions most nearly compatible with given families of conditional distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 377-390, December.
    2. Jens Jensen & Hans Künsch, 1994. "On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 475-486, September.
    3. Ip, Edward H. & Wang, Yuchung J., 2009. "Canonical representation of conditionally specified multivariate discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1282-1290, July.
    4. Levine, Richard A. & Casella, George, 2006. "Optimizing random scan Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2071-2100, November.
    5. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose Maria, 2002. "Exact and near compatibility of discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 231-252, August.
    6. Dobra, Adrian & Hans, Chris & Jones, Beatrix & Nevins, J.R.Joseph R. & Yao, Guang & West, Mike, 2004. "Sparse graphical models for exploring gene expression data," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 196-212, July.
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    Cited by:

    1. Kuo, Kun-Lin & Song, Chwan-Chin & Jiang, Thomas J., 2017. "Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 115-123.
    2. Yao, Yi-Ching & Chen, Shih-chieh & Wang, Shao-Hsuan, 2014. "On compatibility of discrete full conditional distributions: A graphical representation approach," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 1-9.
    3. Farooq, Bilal & Bierlaire, Michel & Hurtubia, Ricardo & Flötteröd, Gunnar, 2013. "Simulation based population synthesis," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 243-263.
    4. Kun-Lin Kuo & Yuchung J. Wang, 2019. "Pseudo-Gibbs sampler for discrete conditional distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 93-105, February.

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