Title: Exploratory and confirmatory Bayesian tests for Gaussian graphical models
Authors: Donald Williams - UC Irvine (United States)
Luis Pericchi - University of Puerto Rico (United States)
Phillip Rast - UC Irvine (United States)
Joris Mulder - Tilburg University (Netherlands) [presenting]
Abstract: Novel statistical methods are introduced for Bayesian hypothesis testing under Gaussian graphical models. These types of models assume a network structure between the outcome variables where an edge between two variables implies a nonzero partial correlation between the respective variables given the other variables. Exploratory Bayes factors are presented for testing whether a partial correlation is zero, positive, or negative. Confirmatory Bayes factors are presented to test specific network structures using equality and/or order constraints on the partial correlations. When the interest is in comparing network structures across multiple independent groups (e.g., a placebo group vs a treatment group) new posterior predictive checks and Bayes factor tests are presented. The Bayes factors are based on proper matrix F priors. The posterior predictive checks are based on the Kullback-Leibler divergence across different network models. The methodology is implemented in the R package BGGM and illustrated in an application on post-traumatic stress disorder.