In this paper, we first propose a Bayesian neighborhood selection method toestimate Gaussian Graphical Models (GGMs). We show the graph selectionconsistency of this method in the sense that the posterior probability of thetrue model converges to one. When there are multiple groups of data available,instead of estimating the networks independently for each group, jointestimation of the networks may utilize the shared information among groups andlead to improved estimation for each individual network. Our method is extendedto jointly estimate GGMs in multiple groups of data with complex structures,including spatial data, temporal data and data with both spatial and temporalstructures. Markov random field (MRF) models are used to efficientlyincorporate the complex data structures. We develop and implement an efficientalgorithm for statistical inference that enables parallel computing. Simulationstudies suggest that our approach achieves better accuracy in networkestimation compared with methods not incorporating spatial and temporaldependencies when there are shared structures among the networks, and that itperforms comparably well otherwise. Finally, we illustrate our method using thehuman brain gene expression microarray dataset, where the expression levels ofgenes are measured in different brain regions across multiple time periods.
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