Constructing priors based on model size for nondecomposable Gaussian graphical models

a simulation based approach

Christopher K. Carter, Frederick Wong, Robert Kohn

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    A method for constructing priors is proposed that allows the off-diagonal elements of the concentration matrix of Gaussian data to be zero. The priors have the property that the marginal prior distribution of the number of nonzero off-diagonal elements of the concentration matrix (referred to below as model size) can be specified flexibly. The priors have normalizing constants for each model size, rather than for each model, giving a tractable number of normalizing constants that need to be estimated. The article shows how to estimate the normalizing constants using Markov chain Monte Carlo simulation and supersedes the method of Wong et al. (2003) [24] because it is more accurate and more general. The method is applied to two examples. The first is a mixture of constrained Wisharts. The second is from Wong et al. (2003) [24] and decomposes the concentration matrix into a function of partial correlations and conditional variances using a mixture distribution on the matrix of partial correlations. The approach detects structural zeros in the concentration matrix and estimates the covariance matrix parsimoniously if the concentration matrix is sparse.
    Original languageEnglish
    Pages (from-to)871-883
    Number of pages13
    JournalJournal of Multivariate Analysis
    Volume102
    Issue number5
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Constrained wishart distribution
    • Gaussian graphical model
    • Multivariate analysis
    • Partial correlations

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