Bayesian Analysis of discrete Bi-directed Graphical Models via Augmented DAG Representation

This paper deals with the Bayesian analysis of discrete bi-directed graphical models. A missing edge in the graph denotes marginal independence between the corresponding variables. The augmented DAG representation of the model is exploited. The augmented model is parameterised in terms of a minimal set of marginal and conditional probability parameters. Compatible priors based on product of Dirichlet Distributions are applied. The prior parameters are specified via a power prior approach. The posterior distributions of the marginal log-linear parameters are obtained using Monte Carlo simulations.