A conjugate prior for discrete hierarchical log-linear models Export

@article{citeulike:5436828, 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.}, archivePrefix = {arXiv}, author = {Massam, H\'{e}l\`{e}ne and Liu, Jinnan and Dobra, Adrian}, citeulike-article-id = {5436828}, citeulike-linkout-0 = {http://arxiv.org/abs/0908.1854}, citeulike-linkout-1 = {http://arxiv.org/pdf/0908.1854}, citeulike-linkout-2 = {http://dx.doi.org/this%20http%20URL}, day = {2}, doi = {this%20http%20URL}, eprint = {0908.1854}, keywords = {convexity, estimation, nonparametric, probability, reduction}, month = {Sep}, posted-at = {2009-08-24 06:00:18}, priority = {3}, title = {A conjugate prior for discrete hierarchical log-linear models}, url = {http://dx.doi.org/this%20http%20URL}, year = {2009} }

TY - JOUR ID - citeulike:5436828 L3 - citeulike-article-id:5436828 N2 - 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. TI - A conjugate prior for discrete hierarchical log-linear models KW - convexity KW - estimation KW - nonparametric KW - probability KW - reduction AU - Massam, Hélène AU - Liu, Jinnan AU - Dobra, Adrian PY - 2009/Sep/02/ UR - http://dx.doi.org/this%20http%20URL ER -