A1145
Title: Junction tree structured Markov random fields with Bernoulli marginals
Authors: Etienne Marceau - Laval University (Canada) [presenting]
Helene Cossette - Laval University (Canada)
Anthony Gelinas - Laval University (Canada)
Abstract: The aim is to investigate the family of junction tree structured Markov random fields with Bernoulli marginal. This allows for a generalization of the tree-based Ising model with improved flexibility in terms of dependence modeling, while retaining the benefits of mean parametrization. An analytic expression is provided for the joint probability mass function of any Bernoulli random vector using moments as parameters, similar to other results found in the literature. This allows for an analytic form for the probability mass function of the studied model. An analytic expression is derived for the joint probability generating function of Bernoulli random vectors encrypted on junction tree structured Markov random fields, along with some applications and algorithms for its computation. The properties of junction trees also allow for a clique-based representation, which yields an efficient sampling algorithm for the model. The estimation of the model is finally assessed from data for a set maximal clique size with maximum likelihood estimation and an analysis on the complexity of the model. The necessary algorithms are provided to estimate models and a numerical example using precipitation data in a high dependence context.
