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

• 成果类型: Article
• 署名作者: Dobra, Adrian; Lenkoski, Alex; Rodriguez, Abel
• 署名单位: University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle; Ruprecht Karls University Heidelberg; University of California System; University of California Santa Cruz
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2011.tm10465
• 发表日期: 2011
• 页码: 1418-1433
• 关键词: inverse wishart distributions; cancer-mortality counts; statistical-analysis; selection; specification; computation; simulation; prediction; likelihood; hastings

摘要

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.