A0209
Title: Classes of multivariate and space-time power-law covariance functions
Authors: Pulong Ma - Iowa State University (United States) [presenting]
Abstract: Understanding marginal covariance and cross-covariance structures is essential for modelling continuously indexed multivariate and space-time processes. The Matern covariance function with short-range dependence has enabled several notable developments for multivariate and space-time models in the past few decades. However, many geophysical methods possess long-range dependence in space and space-time domains, which the Matern-based covariance models often fail to capture. The purpose is to exploit a scale-mixture framework to address this issue to construct new classes of multivariate and space-time covariance functions with power-law decay in the tail. This framework generates a covariance function by mixing over a base covariance model with a probability measure. Sufficient and necessary conditions are established to characterize the relationship between the behaviour of resultant covariance functions and the mixing probability measure. Then theoretical properties of the resultant covariance models are investigated. Several validity conditions that ensure the positive definiteness of the proposed multivariate covariance models are derived. The interplay among long-range dependence, Markov property, and screening effect are examined theoretically. Extensive simulation examples and real datasets are used to illustrate the superior performance of the proposed covariance models over the state-of-the-art models.
