David Bolin: Multivariate normal inverse Gaussian Matérn fields

Abstract: We present a new class of multivariate random fields with Matérn covariance functions and with multivariate marginal distributions that are more flexible than the Gaussian distribution. The fields are obtained as solutions to systems of stochastic partial differential equations (SPDEs) driven by normal inverse Gaussian (NIG) noise. We show that there are many different multivariate differential operators that result in equivalent multivariate random fields if Gaussian noise is used in the SPDEs, and characterise a class of such equivalent operators. In combination with NIG noise this class defines a class of multivariate random fields with equivalent cross-covariance structure but different multivariate marginal distributions, whose shape are controlled by parameters in the operator. The models are incorporated in a geostatistical setting with measurement errors and covariates, and a computationally efficient likelihood-based parameter estimation method is derived. Finally, we show that the models have better predictive performance than standard Gaussian models for a popular multivariate geostatistical dataset.