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Article overview
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Bayesian precision matrix estimation for graphical Gaussian models with edge and vertex symmetries | | Helene Massam
; Qiong Li
; Xin Gao
; | | Date: |
14 Jun 2015 | | Abstract: | Graphical Gaussian models with edge and vertex symmetries were introduced by
citet{HojLaur:2008} who also gave an algorithm to compute the maximum
likelihood estimate of the precision matrix for such models. In this paper, we
take a Bayesian approach to the estimation of the precision matrix. We consider
only those models where the symmetry constraints are imposed on the precision
matrix and which thus form a natural exponential family with the precision
matrix as the canonical parameter.
We first identify the Diaconis-Ylvisaker conjugate prior for these models and
develop a scheme to sample from the prior and posterior distributions. We thus
obtain estimates of the posterior mean of the precision matrix.
Second, in order to verify the precision of our estimate, we derive the
explicit analytic expression of the expected value of the precision matrix when
the graph underlying our model is a tree, a complete graph on three vertices
and a decomposable graph on four vertices with various symmetries. In those
cases, we compare our estimates with the exact value of the mean of the prior
distribution. We also verify the accuracy of our estimates of the posterior
mean on simulated data for graphs with up to thirty vertices and various
symmetries. | | Source: | arXiv, 1506.4347 | | Services: | Forum | Review | PDF | Favorites | |
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