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This paper focuses on vector random fields defined on Sd x Rk, d ≤ 2 and k ≤ 1, with covariance functions that depend on the geodesic distance in Sd and on the separation vector in Rk. First, we propose parametric families of nonseparable covariance functions with closed-form expressions and explicit spectral representations. Then, we derive an algorithm for fast simulation of such random fields, which combines spectral simulation methods in Sd and Rk previously introduced in the literature and relies on importance sampling techniques. We provide computer codes and practical guidelines and describe the advantages of our proposal in comparison to other methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of simulating a Gaussian random vector with zero mean and given variance–covariance matrix, without conditioning constraints. Variants of the Gibbs sampler algorithm are presented, based on the proposal by Galli and Gao, which do not require inverting the variance–covariance matrix and therefore allow considerable time savings. Numerical experiments are performed to check the accuracy of the algorithm and to determine implementation parameters (in particular, the updating and blocking strategies) that increase the rates of convergence and mixing. [Copyright &y& Elsevier]