On joint estimation of Gaussian graphical models for spatial and temporal data

Zhixiang Lin, Tao Wang, Can YANG, Hongyu Zhao*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

25 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)769-779
Number of pages11
Issue number3
Publication statusPublished - Sept 2017

Scopus Subject Areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

User-Defined Keywords

  • Bayesian variable selection
  • Gaussian graphical model
  • Markov random field
  • Neighborhood selection
  • Spatial and temporal data


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