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Abstract:
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Graphical models describe the conditional independence relations in multivariate data. They are used for a variety of problems, including log-linear models, network analysis, and genetics. A distribution that satisfies the conditional independence structure of a graph is Markov. A graphical model is a family of distributions that are Markov with respect to a certain graph. In a Bayesian problem, one may specify a prior over the graphical model. Such a prior is a hyper Markov law if the random marginals also satisfy the independence constraints. Previous work in this area focused on parametric models. In this paper, I extend the theory to graphical models based on a nonparametric family, the Dirichlet processes. I prove sufficient conditions for a Dirichlet process to be hyper Markov using a stick-breaking construction. This work is applicable to other stick-breaking priors.
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