Simulation of Intrinsic Random Fields of Order $$k$$ k with Gaussian Generalized Increments by Gibbs Sampling

Abstract

This work pertains to the simulation of an intrinsic random field of order $$k$$ with a given generalized covariance function and multivariate Gaussian generalized increments. An iterative algorithm based on the Gibbs sampler is proposed to simulate such a random field at a finite set of locations, resulting in a sequence of random vectors that converges in distribution to a random vector with the desired distribution. The algorithm is tested on synthetic case studies to experimentally assess its rate of convergence, showing that few iterations are sufficient for convergence to take place. The sequence of random vectors also proves to be strongly mixing, allowing the generation of as many independent realizations as desired with a single run of the algorithm. Another interesting property of this algorithm is its versatility, insofar as it can be adapted to construct realizations conditioned to pre-existing data and can be used for any number and configuration of the target locations and any generalized covariance model.