Graphical Models in Reconstructability Analysis and Bayesian Networks

Introduction to Graphical Models, Hidden Markov Models and Bayesian Networks

Bayesian analysis of matrix normal graphical models.

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Ext...

Cuts in Bayesian graphical models

The cut function defined by theOpenBUGS software is described as a “valve” that prevents feedback in Bayesian graphical models. It is shown that theMCMC algorithm applied by OpenBUGS in the presence of a cut function does not converge to a well-defined limiting distribution. However, it may be improved by using tempered transitions. The cut algorithm is compared with multiple imputation as a go...

Graphical Reasoning with Bayesian Networks

Nowadays, Bayesian networks are seen by many researchers as standard tools for reasoning with uncertainty. Despite the fact that Bayesian networks are graphical representations, representing dependence and independence information, normally the emphasis of the visualisation of the reasoning process is on showing changes in the associated marginal probability distributions due to entering observ...

Bayesian structure learning in graphical models

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension p exceeds the sample size n. Gaussian graphical models provide an important tool in describing conditional independence through presence or absence of the edges in the underlying graph. A popular non-Bayesian method of estimating a graphical structure i...