Equivalence class selection of categorical graphical models

Learning the structure of dependence relations between variables is a pervasive issue in statistical literature. A directed acyclic graph (DAG) can represent set conditional independencies, but different DAGs may encode same and are indistinguishable using observational data. Equivalent be collected into classes, each represented by partially known as essential (EG). Structure learning directly conducted on EG space, rather than allied space DAGs, leads to theoretical computational benefits. Still, majority efforts has been dedicated Gaussian data, with less attention methods designed for multivariate categorical Bayesian methodology EGs then proposed. Combining constructive parameter prior elicitation graph-driven likelihood decomposition, closed-form expression marginal model derived. Asymptotic properties studied, an MCMC sampler scheme developed approximate posterior inference. The evaluated both simulated scenarios real appreciable performance comparison state-of-the-art methods.