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Compatibility of discrete conditional distributions with structural zeros

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  • Wang, Yuchung J.
  • Kuo, Kun-Lin

Abstract

A general algorithm is provided for determining the compatibility among full conditionals of discrete random variables with structural zeros. The algorithm is scalable and it can be implemented in a fairly straightforward manner. A MATLAB program is included in the Appendix and therefore, it is now feasible to check the compatibility of multi-dimensional conditional distributions with constrained supports. Rather than the linear equations in the restricted domain of Arnold et al. (2002) [11] Tian et al. (2009) [16], the approach is odds-oriented and it is a discrete adaptation of the compatibility check of Besag (1994) [17]. The method naturally leads to the calculation of a compatible joint distribution or, in the absence of compatibility, a nearly compatible joint distribution. Besag's [5] factorization of a joint density in terms of conditional densities is used to justify the algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:191-199
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    References listed on IDEAS

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    1. Kaiser, Mark S. & Cressie, Noel, 2000. "The Construction of Multivariate Distributions from Markov Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 199-220, May.
    2. 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.
    3. Arnold, Barry C. & Gokhale, D. V., 1994. "On uniform marginal representation of contingency tables," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 311-316, November.
    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. 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.
    2. Kun-Lin Kuo & Yuchung J. Wang, 2023. "Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.
    3. 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.

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