Structural Markov graph laws for Bayesian model uncertainty

Abstract

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov properties, for both undirected decomposable and directed acyclic graphs, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This allows the analysis and comparison of multiple graphical structures, while being able to take advantage of the common conditional independence constraints. Moreover, we show that these properties characterise exponential families, which form conjugate priors under sampling from compatible Markov distributions.

Published at http://dx.doi.org/10.1214/15-AOS1319 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• A Transformational Characterization of Equivalent Bayesian Network Structures
• Wishart distributions for decomposable graphs
• Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs
• On the Construction of the Inclusion Boundary Neighbourhood for Markov Equivalence Classes of Bayesian Network Structures

Cited by in corpus (1)

• A closed-form approach to Bayesian inference in tree-structured graphical models