Graphical Gaussian process models for highly multivariate spatial data

• 成果类型: Article
• 署名作者: Dey, Debangan; Datta, Abhirup; Banerjee, Sudipto
• 署名单位: Johns Hopkins University; Johns Hopkins Bloomberg School of Public Health; University of California System; University of California Los Angeles
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asab061
• 发表日期: 2022
• 页码: 9931014
• 关键词: cross-covariance functions; decomposable graphs; random-fields; inference

摘要

For multivariate spatial Gaussian process models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence between the variables. This is undesirable, especially in highly multivariate settings, where popular cross-covariance functions, such as multivariate Matern functions, suffer from a curse of dimensionality as the numbers of parameters and floating-point operations scale up in quadratic and cubic order, respectively, with the number of variables. We propose a class of multivariate graphical Gaussian processes using a general construction called stitching that crafts cross-covariance functions from graphs and ensures process-level conditional independence between variables. For the Matern family of functions, stitching yields a multivariate Gaussian process whose univariate components are Matern Gaussian processes, and which conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Matern Gaussian process to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.