2008/07/22 by Daniel Heinz, Heinz, Daniel
Computer Science · #36E05 (Primary) 62G99 (Secondary) #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Mathematics #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.0807.3410
openalex publication_date 2008/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt, 1981; Strauss and Ikeda, 1990; Wasserman and Pattison, 1996; Pattison and Wasserman, 1999; Robins et al., 1999);, graphical Gaussian models (Roverato and Whittaker, 1998; Giudici and Green, 1999; Marrelec and Benali, 2006), and genetics (Dobra et al., 2004). A distribution that satisfies the conditional independence structure of a graph is Markov. A graphical model is a family of distributions that is restricted to be Markov with respect to a certain graph. In a Bayesian problem, one may specify a prior over the graphical model. Such a prior is called a hyper Markov law if the random marginals also satisfy the independence constraints. Previous work in this area includes (Dempster, 1972; Dawid and Lauritzen, 1993; Giudici and Green, 1999; Letac and Massam, 2007). We explore graphical models based on a non-parametric family of distributions, developed from Dirichlet processes.