Undirected Structural Markov Property for Bayesian Model Determination

Xiong Kang, Yingying Hu and Yi Sun ()
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Xiong Kang: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
Yingying Hu: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
Yi Sun: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Mathematics, 2023, vol. 11, issue 7, 1-22

Abstract: This paper generalizes the structural Markov properties for undirected decomposable graphs to arbitrary ones. This helps us to exploit the conditional independence properties of joint prior laws to analyze and compare multiple graphical structures, while being able to take advantage of the common conditional independence constraints. This work provides a theoretical support for full Bayesian posterior updating about the structure of a graph using data from a certain distribution. We further investigate the ratio of graph law so as to simplify the acceptance probability of the Metropolis–Hastings sampling algorithms.

Keywords: graphical model; structural Markov law; Bayesian inference; model determination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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