deepspat: An R package for modeling nonstationary spatial and spatio-temporal Gaussian and extremes data through deep deformations

TL;DR

deepspat is an R package that enables modeling, fitting, and prediction of nonstationary spatial and spatio-temporal Gaussian and extremes data using deep deformation techniques, facilitated by automatic differentiation.

Contribution

The paper introduces deepspat, a novel R package that implements nonstationary models via deep domain deformations, filling a gap in available statistical software.

Findings

Successfully modeled nonstationary temperature data in Nepal.

Demonstrated the effectiveness of deep deformations in capturing nonstationarity.

Validated the approach through simulation studies.

Abstract

Nonstationarity in spatial and spatio-temporal processes is ubiquitous in environmental datasets, but is not often addressed in practice, due to a scarcity of statistical software packages that implement nonstationary models. In this article, we introduce the R software package deepspat, which allows for modeling, fitting and prediction with nonstationary spatial and spatio-temporal models applied to Gaussian and extremes data. The nonstationary models in our package are constructed using a deep multi-layered deformation of the original spatial or spatio-temporal domain, and are straightforward to implement. Model parameters are estimated using gradient-based optimization of customized loss functions with tensorflow, which implements automatic differentiation. The functionalities of the package are illustrated through simulation studies and an application to Nepal temperature data.