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On compatibility of discrete full conditional distributions: A graphical representation approach

Author

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  • Yao, Yi-Ching
  • Chen, Shih-chieh
  • Wang, Shao-Hsuan

Abstract

To deal with the compatibility issue of full conditional distributions of a (discrete) random vector, a graphical representation is introduced where a vertex corresponds to a configuration of the random vector and an edge connects two vertices if and only if the ratio of the probabilities of the two corresponding configurations is specified through one of the given full conditional distributions. Compatibility of the given full conditional distributions is equivalent to compatibility of the set of all specified probability ratios (called the ratio set) in the graphical representation. Characterizations of compatibility of the ratio set are presented. When the ratio set is compatible, the family of all probability distributions satisfying the specified probability ratios is shown to be the set of convex combinations of k probability distributions where k is the number of components of the underlying graph.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:1-9
    DOI: 10.1016/j.jmva.2013.10.007
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    References listed on IDEAS

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    1. Wang, Yuchung J. & Kuo, Kun-Lin, 2010. "Compatibility of discrete conditional distributions with structural zeros," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 191-199, January.
    2. 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.
    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. 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.
    5. Kuo, Kun-Lin & Wang, Yuchung J., 2011. "A simple algorithm for checking compatibility among discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2457-2462, August.
    6. 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.
    7. A. Gelman & T. P. Speed, 1999. "Corrigendum: Characterizing a joint probability distribution by conditionals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 483-483, April.
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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.

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