Open Access
Translator Disclaimer
August 2015 Structural Markov graph laws for Bayesian model uncertainty
Simon Byrne, A. Philip Dawid
Ann. Statist. 43(4): 1647-1681 (August 2015). DOI: 10.1214/15-AOS1319


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.


Download Citation

Simon Byrne. A. Philip Dawid. "Structural Markov graph laws for Bayesian model uncertainty." Ann. Statist. 43 (4) 1647 - 1681, August 2015.


Received: 1 March 2014; Revised: 1 January 2015; Published: August 2015
First available in Project Euclid: 17 June 2015

zbMATH: 1317.62046
MathSciNet: MR3357874
Digital Object Identifier: 10.1214/15-AOS1319

Primary: 62H05
Secondary: 05C80 , 05C90 , 68T30

Keywords: graphical models , hyper Markov laws , structural estimation , structural Markov laws

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 4 • August 2015
Back to Top