Think continuous: Markovian Gaussian models in spatial statistics

TL;DR

This paper explores the connection between Markovian Gaussian random fields and GMRFs, emphasizing their computational efficiency and interpretability for modeling complex spatial phenomena.

Contribution

It clarifies the theoretical link and practical implementation of continuous Markovian Gaussian fields, enhancing spatial statistical modeling capabilities.

Findings

Efficient computation methods for continuous Markovian Gaussian fields.

Advantages in modeling anisotropy and non-stationarity.

Improved interpretability of spatial models.

Abstract

Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as the Markov property is difficult to deploy in continuous space. Following the pioneering work of Lindgren et al. (2011), we expound on the link between Markovian Gaussian random fields and GMRFs. In particular, we discuss the theoretical and practical aspects of fast computation with continuously specified Markovian Gaussian random fields, as well as the clear advantages they offer in terms of clear, parsimonious and interpretable models of anisotropy and non-stationarity.