Open Access
December 2009 A conjugate prior for discrete hierarchical log-linear models
Hélène Massam, Jinnan Liu, Adrian Dobra
Ann. Statist. 37(6A): 3431-3467 (December 2009). DOI: 10.1214/08-AOS669


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.


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Hélène Massam. Jinnan Liu. Adrian Dobra. "A conjugate prior for discrete hierarchical log-linear models." Ann. Statist. 37 (6A) 3431 - 3467, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1369.62048
MathSciNet: MR2549565
Digital Object Identifier: 10.1214/08-AOS669

Primary: 62E15 , 62F15 , 62H17

Keywords: conjugate prior , Contingency tables , Hierarchical log-linear models , hyper Dirichlet , hyper Markov property , Model selection

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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