Multivariate type G Matern stochastic partial differential equation random fields

• 成果类型: Article
• 署名作者: Bolin, David; Wallin, Jonas
• 署名单位: King Abdullah University of Science & Technology; University of Gothenburg; Lund University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12351
• 发表日期: 2020
• 页码: 215-239
• 关键词: cross-covariance functions; vector random-fields; Scoring rules; models

摘要

For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matern type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula-based models. In contrast with these, the last two constructions can model non-Gaussian spatial data without replicates. Computationally efficient methods for likelihood-based parameter estimation and probabilistic prediction are proposed, and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications.