Fundamentals of statistical exponential families: with applications in statistical decision theory
Fundamentals of statistical exponential families: with applications in statistical decision theory
Parallell interacting MCMC for learning of topologies of graphical models
Data Mining and Knowledge Discovery
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Bayesian model determination in the complete class of graphical models is considered using a decision theoretic framework within the regular exponential family. The Complete class contains both decomposable and non-decomposable graphical models. A utility measure based on a logarithmic score function is introduced under reference priors for the model parameters. The logarithmic utility of a model is decomposed into predictive performance and relative complexity. Axioms of decision theory lead to the judgement of the plausibility of a model in terms of the posterior expected utility. This quantity has an analytic expression for decomposable models when certain reference priors are used and the exponential family is closed under marginalization. For non-decomposable models, a simulation consistent estimate of the expectation can be obtained. Both real and simulated data sets are used to illustrate the introduced methodology.