A CONJUGATE PRIOR FOR DISCRETE HIERARCHICAL LOG-LINEAR MODELS

• 成果类型: Article
• 署名作者: Massam, Helene; Liu, Jinnan; Dobra, Adrian
• 署名单位: York University - Canada; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS669
• 发表日期: 2009
• 页码: 3431-3467
• 关键词: Graphical models

摘要

In Bayesian analysis of multi-way contingency tables, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These priors are defined as the Diaconis-Ylvisaker conjugate priors on the log-linear parameters subject to baseline constraints under multinomial sampling. We also derive the induced prior on the cell probabilities and show that the induced prior is a generalization of the hyper Dirichlet prior. We show that this prior has several desirable properties and illustrate its Usefulness by identifying the most probable decomposable, graphical and hierarchical log-linear models for a six-way contingency table.