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A CONJUGATE PRIOR FOR DISCRETE HIERARCHICAL LOG-LINEAR MODELS

Hélène Massam, Jinnan Liu and Adrian Dobra
The Annals of Statistics
Vol. 37, No. 6A (December 2009), pp. 3431-3467
Stable URL: http://www.jstor.org/stable/25662199
Page Count: 37
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A CONJUGATE PRIOR FOR DISCRETE HIERARCHICAL LOG-LINEAR MODELS
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Abstract

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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