A conjugate prior for discrete hierarchical log-linear models

Details A conjugate prior for discrete hierarchical log-linear models A conjugate prior for discrete hierarchical log-linear models

2007-11-10

arxiv.org/abs/0711.1609v3

Annals of Statistics 2009, Vol. 37, No. 6A, 3431-3467

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS669 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A conjugate prior for discrete hierarchical log-linear models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A conjugate prior for discrete hierarchical log-linear models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A conjugate prior for discrete hierarchical log-linear models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-27758