Building hyper Dirichlet processes for graphical models

• DOI: 10.1214/08-ejs269
• Publication Date: 2009-04-10T06:59:51Z
• Authors: Daniel Heinz
• Keywords: 36E05; Mathematics - Statistics Theory; decomposable graphical distribution; Statistics Theory (math.ST); 01 natural sciences; non-parametric prior; Hyper Markov law; FOS: Mathematics; covariance selection; stick-breaking measure; 0101 mathematics; 62G99; 36E05 (Primary) 62G99 (Secondary)

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.<br/>Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)<br/>