title: On joint estimation of Gaussian graphical models for spatial and temporal data.
abstract: In this article, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model converges to one. When there are multiple groups of data available, instead of estimating the networks independently for each group, joint estimation of the networks may utilize the shared information among groups and lead to improved estimation for each individual network. Our method is extended to jointly estimate GGMs in multiple groups of data with complex structures, including spatial data, temporal data, and data with both spatial and temporal structures. Markov random field (MRF) models are used to efficiently incorporate the complex data structures. We develop and implement an efficient algorithm for statistical inference that enables parallel computing. Simulation studies suggest that our approach achieves better accuracy in network estimation compared with methods not incorporating spatial and temporal dependencies when there are shared structures among the networks, and that it performs comparably well otherwise. Finally, we illustrate our method using the human brain gene expression microarray dataset, where the expression levels of genes are measured in different brain regions across multiple time periods.
authors.affiliation: Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut, U.S.A.|Department of Statistics, Stanford University, Stanford, California, U.S.A.
authors.forename: Zhixiang
authors.initials: Z
authors.lastname: Lin
authors.affiliation: Department of Bioinformatics and Biostatistics, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Wang
authors.affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
authors.forename: Can
authors.initials: C
authors.lastname: Yang
authors.affiliation: Department of Biostatistics, School of Public Health, Yale University, New Haven, Connecticut, U.S.A.
authors.forename: Hongyu
authors.initials: H
authors.lastname: Zhao
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D015233:Models, Statistical; D016011:Normal Distribution
keywords: Bayesian variable selection; Gaussian graphical model; Markov random field; Neighborhood selection; Spatial and temporal data