Abstract not found

Abstract not found

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. 1. Introduction. We

A Bayesian methodology for estimating the size of a closed population from multiple incomplete administrative lists is proposed. The approach allows for a variety of dependence structures between the lists, inclusion of covariates, and explicitly accounts for model uncertainty. Interval estimates from this approach are compared to frequentist and previously published Bayesian approaches, and found to be superior. Several examples are considered. KEYWORDS: Bayesian graphical model; Capture-recapture; Closed population estimation; Chordal graph; Contingency table; Decomposable log-linear model; Markov distribution. Contents