A Multi-Resolution Spatial Model for Large Datasets Based on the Skew-t Distribution

TL;DR

This paper introduces a novel multi-resolution spatial model based on the skew-t distribution, enabling flexible modeling of large, non-Gaussian environmental datasets with dependence at multiple scales.

Contribution

It presents the first multi-resolution spatial model using skew-t distributions, combining large-scale normal effects with fine-scale skew-normal effects for better data representation.

Findings

Successfully modeled daily wind speeds over Saudi Arabia.

Demonstrated improved fit for skewness and heavy tails.

Feasible inference via Monte Carlo EM algorithm.

Abstract

Large, non-Gaussian spatial datasets pose a considerable modeling challenge as the dependence structure implied by the model needs to be captured at different scales, while retaining feasible inference. Skew-normal and skew-t distributions have only recently begun to appear in the spatial statistics literature, without much consideration, however, for the ability to capture dependence at multiple resolutions, and simultaneously achieve feasible inference for increasingly large data sets. This article presents the first multi-resolution spatial model inspired by the skew-t distribution, where a large-scale effect follows a multivariate normal distribution and the fine-scale effects follow a multivariate skew-normal distributions. The resulting marginal distribution for each region is skew-t, thereby allowing for greater flexibility in capturing skewness and heavy tails characterizing many environmental datasets. Likelihood-based inference is performed using a Monte Carlo EM algorithm. The model is applied as a stochastic generator of daily wind speeds over Saudi Arabia.