Graph-based multivariate conditional autoregressive models

作     者：Ye Liang 

作者机构：Department of StatisticsOklahoma State UniversityStillwaterOklahoma 74078USA 

出 版 物：《Statistical Theory and Related Fields》 (统计理论及其应用（英文）)

年 卷 期：2019年第3卷第2期

页      面：158-169页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Areal data disease mapping graphical model G-wishart distribution Markov random field reversible jump 

摘      要：The conditional autoregressive model is a routinely used statistical model for areal data thatarise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have also been extensively studied in the literatureand it has been shown that extending from the univariate case to the multivariate case is nottrivial. The difficulties lie in many aspects, including validity, interpretability, flexibility and computational feasibility of the model. In this paper, we approach the multivariate modelling froman element-based perspective instead of the traditional vector-based perspective. We focus onthe joint adjacency structure of elements and discuss graphical structures for both the spatialand non-spatial domains. We assume that the graph for the spatial domain is generally knownand fixed while the graph for the non-spatial domain can be unknown and random. We proposea very general specification for the multivariate conditional modelling and then focus on threespecial cases, which are linked to well-known models in the literature. Bayesian inference forparameter learning and graph learning is provided for the focused cases, and finally, an examplewith public health data is illustrated.