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

Yi Ching Yao, Shih chieh Chen, Shao Hsuan Wang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalJournal of Multivariate Analysis
Volume124
DOIs
StatePublished - Feb 2014

Keywords

  • Connected graph
  • Full conditional
  • Graph theory
  • Primary
  • Secondary
  • Spanning tree

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