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A simple algorithm for checking compatibility among discrete conditional distributions

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  • Kuo, Kun-Lin
  • Wang, Yuchung J.

Abstract

A distribution is said to be conditionally specified when only its conditional distributions are known or available. The very first issue is always compatibility: does there exist a joint distribution capable of reproducing all of the conditional distributions? We review five methods-mostly for two or three variables-published since 2002, and we conclude that these methods are either mathematically too involved and/or are too difficult (and in many cases impossible) to generalize to a high dimension. The purpose of this paper is to propose a general algorithm that can efficiently verify compatibility in a straightforward fashion. Our method is intuitively simple and general enough to deal with any full-conditional specifications. Furthermore, we illustrate the phenomenon that two theoretically equivalent conditional models can be different in terms of compatibilities, or can result in different joint distributions. The implications of this phenomenon are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:8:p:2457-2462
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. repec:ags:afjare:141665 is not listed on IDEAS
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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. 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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