Canonical representation of conditionally specified multivariate discrete distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Ip, Edward H.^1,2  Wang, Yuchung J.³ 

[1] Wake Forest Univ, Sch Med, Dept Biostat Sci, Winston Salem, NC 27157 USA

[2] Wake Forest Univ, Dept Social Sci & Hlth Policy, Sch Med, Winston Salem, NC 27157 USA

[3] Rutgers State Univ, Dept Math Sci, Camden, NJ 08102 USA

关键词: Canonical parameter;    Characterizing set of interactions;    Compatibility check;    Exponential family;    Near-compatible;    Pseudo-Gibbs sampler;   

DOI  :  10.1016/j.jmva.2008.11.010

来源: Elsevier

【 摘 要 】

Most work on conditionally specified distributions has focused on approaches that operate on the probability space, and the constriants on the probability space often make the study of their properties challenging. We propose decomposing both the joint and conditional discrete distributions in to characterizing sets of canonical interactions, and we prove that certain interactions of a joint distribution are shared with its conditional distributions. This invariance opens the door for checking the compatibility between conditional distributions involving the same set of variables. We formulate necessary and sufficient conditions for the existence and uniqueness of discrete conditional models, and we show how a joint distribution can be easily computed from the pool of interactions collected form the conditional distributions. Hence, the methods can be used to calculate the exact distributions of a Gibbs sampler. Furthermore, issues such as how near compability can be reconciled are also discussed. Using mixed parameterization, we show that the proposed approach is based on the canonical parameters, while the conventional approaches are based on the mean parameters. Our advantage is partly due to the invariance that holds only for the canonical parameters. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free