Electronic Journal of Statistics

Building hyper Dirichlet processes for graphical models

Daniel Heinz

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 3 (2009), 290-315.

Dates
First available in Project Euclid: 14 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1239716415

Digital Object Identifier
doi:10.1214/08-EJS269

Mathematical Reviews number (MathSciNet)
MR2495840

Zentralblatt MATH identifier
1326.62012

Subjects
Primary: 36E05
Secondary: 62G99: None of the above, but in this section

Keywords
Hyper Markov law stick-breaking measure non-parametric prior decomposable graphical distribution covariance selection

Citation

Heinz, Daniel. Building hyper Dirichlet processes for graphical models. Electron. J. Statist. 3 (2009), 290--315. doi:10.1214/08-EJS269. https://projecteuclid.org/euclid.ejs/1239716415


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