A unified method for checking compatibility and uniqueness for finite discrete conditional distributions

Guo Liang Tian*, Ming Tan, Kai Wang Ng, Man Lai TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Checking compatibility for two given conditional distributions and identifying the corresponding unique compatible marginal distributions are important problems in mathematical statistics, especially in Bayesian inferences. In this article, we develop a unified method to check the compatibility and uniqueness for two finite discrete conditional distributions. By formulating the compatibility problem into a system of linear equations subject to constraints, it can be reduced to a quadratic optimization problem with box constraints. We also extend the proposed method from two-dimensional cases to higher-dimensional cases. Finally, we show that our method can be easily applied to checking compatibility and uniqueness for a regression function and a conditional distribution. Several numerical examples are used to illustrate the proposed method. Some comparisons with existing methods are also presented.

Original languageEnglish
Pages (from-to)115-129
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Volume38
Issue number1
DOIs
Publication statusPublished - Jan 2009

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • 2-norm
  • Box constraints
  • Compatibility
  • Gibbs sampler
  • Kullback-Leibler distance
  • Quadratic optimization with constraints

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