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. 2011;106(496):1418-1433.
doi: 10.1198/jasa.2011.tm10465. Epub 2012 Dec 24.

Bayesian Inference for General Gaussian Graphical Models With Application to Multivariate Lattice Data

Adrian Dobra  1 , Alex Lenkoski  2 , Abel Rodriguez  3
Affiliations

Bayesian Inference for General Gaussian Graphical Models With Application to Multivariate Lattice Data

Adrian Dobra et al. J Am Stat Assoc. 2011.

Abstract

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using a simulated example and a real-world application which concerns cancer mortality surveillance. Supplementary materials with computer code and the datasets needed to replicate our numerical results together with additional tables of results are available online.

Keywords: CAR model; G-Wishart distribution; Markov chain Monte Carlo (MCMC) simulation; Spatial statistics.

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Figures

Figure 1
Figure 1
Mortality rates (per 10,000 habitants) in the 48 continental states and the D.C. area corresponding to four common cancers during 2000.
Figure 2
Figure 2
Convergence plot of the average size of the column graph GC by log iteration for model GGM-U (left panel) and model GGM-S (right panel).
Figure 3
Figure 3
Edge inclusion probabilities for model GGM-U (lower triangle) and model GGM-S (upper triangle) in the U.S. cancer mortality example. The acronyms used are explained in the Supplementary Materials.
See this image and copyright information in PMC

References

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    1. Banerjee O, El Ghaoui L, D’Aspremont A. Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data. Journal of Machine Learning Research. 2008;9:485–516.

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