A Bayesian framework for structural learning of mixed graphical models

Graphical models provide an effective tool to represent conditional independences among variables. While this class of models has been extensively studied in the Gaussian and categorical settings separately, literature which combines the two types of variables is narrow. However, mixed data are extremely diffuse in many applications where both continuous and categorical measurements are available. In this paper we propose a Bayesian framework for the analysis of mixed data. Specifically, we specifiy a likelihood function for n observations following a conditional Gaussian distribution, and assign suitable priors for the model parameters. Our end-result is a closed form espression for the marginal data distribution. The latter provides a primary input for the computation of the marginal likelihood under graph (independence) constraints and the development of an MCMC strategy for graph structural learning.