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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:124

Article

Yao, Yi-Ching^1,2  Chen, Shih-Chieh²  Wang, Shao-Hsuan³ 

[1] Acad Sinica, Inst Stat Sci, Taipei 115, Taiwan

[2] Natl Chengchi Univ, Dept Stat, Taipei 116, Taiwan

[3] Natl Taiwan Univ, Dept Math, Taipei 106, Taiwan

关键词: Connected graph;    Full conditional;    Graph theory;    Spanning tree;   

DOI  :  10.1016/j.jmva.2013.10.007

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

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