Generalized Gaussian Random Fields using hidden selections

TL;DR

This paper introduces selection Gaussian random fields, a non-Gaussian model capable of capturing skewness, multi-modality, and heavy tails, with algorithms for simulation and parameter estimation demonstrated on synthetic and seismic data.

Contribution

It presents a novel class of non-Gaussian random fields and efficient algorithms for their simulation and parameter estimation, improving predictive performance.

Findings

Reduced mean square prediction error by 20-40% on seismic data.

Effectively captures skewness, multi-modality, and heavy tails.

Provides more reliable prediction intervals.

Abstract

We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy tails in the marginal distribution. We present a Metropolis-Hastings algorithm for efficient simulation of realizations from the random field, and a numerical algorithm for estimating model parameters by maximum likelihood. The algorithms are demonstrated and evaluated on synthetic cases and on a real seismic data set from the North Sea. In the North Sea data set we are able to reduce the mean square prediction error by 20-40% compared to a Gaussian model, and we obtain more reliable prediction intervals.