A conjugate prior for discrete hierarchical log-linear models

Massam, Hélène ; Liu, Jinnan ; Dobra, Adrian

Ann. Statist., Tome 37 (2009) no. 1, p. 3431-3467 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2009-12-15
Classification:  Hierarchical log-linear models,  conjugate prior,  contingency tables,  hyper Markov property,  hyper Dirichlet,  model selection,  62F15,  62H17,  62E15