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September 2013 On the Prior and Posterior Distributions Used in Graphical Modelling
Marco Scutari
Bayesian Anal. 8(3): 505-532 (September 2013). DOI: 10.1214/13-BA819


Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model are estimated conditional on that graph structure. While the probability distributions involved in this second step have been studied in depth, the ones used in the first step have not been explored in as much detail.

In this paper, we will study the prior and posterior distributions defined over the space of the graph structures for the purpose of learning the structure of a graphical model. In particular, we will provide a characterisation of the behaviour of those distributions as a function of the possible edges of the graph. We will then use the properties resulting from this characterisation to define measures of structural variability for both Bayesian and Markov networks, and we will point out some of their possible applications.


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Marco Scutari. "On the Prior and Posterior Distributions Used in Graphical Modelling." Bayesian Anal. 8 (3) 505 - 532, September 2013.


Published: September 2013
First available in Project Euclid: 9 September 2013

zbMATH: 1329.62145
MathSciNet: MR3102220
Digital Object Identifier: 10.1214/13-BA819

Rights: Copyright © 2013 International Society for Bayesian Analysis


Vol.8 • No. 3 • September 2013
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