Non-Gaussian Geostatistical Modeling using (skew) t Processes

TL;DR

This paper introduces a novel non-Gaussian geostatistical model using (skew) t processes to better capture heavy tails and asymmetry in spatial data, with applications demonstrated on Australian temperature data.

Contribution

It develops a new (skew) t process model for spatial data, including analytic properties and estimation methods, advancing non-Gaussian geostatistical modeling.

Findings

Weighted pairwise likelihood effectively estimates the model parameters.

The (skew) t process outperforms Gaussian models in predictive accuracy.

Application to temperature data demonstrates practical utility.

Abstract

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) $t$ process we study the second-order and geometrical properties and in the $t$ case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the $t$ process. Moreover we compare the performance of the optimal linear predictor of the $t$ process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia