# Bayesian Modeling for Nonstationary Spatial Point Process via Spatial Deformations

## TL;DR

This paper introduces a Bayesian method for modeling nonstationary spatial point processes using spatial deformations, showing improved performance on both synthetic and real-world data.

## Contribution

The novel contribution is a data-driven spatial deformation approach for nonstationary spatial Cox processes, enhanced with Hamiltonian Monte Carlo for efficient Bayesian inference.

## Key findings

- The proposed method outperformed alternative anisotropic formulations in synthetic data experiments.
- The real-world application on pest spread in Brazil demonstrated the practical benefits of the new approach.
- Hamiltonian Monte Carlo improved computational efficiency compared to traditional MCMC methods.

## Abstract

Many techniques have been proposed to model space-varying observation processes with a nonstationary spatial covariance structure and/or anisotropy, usually on a geostatistical framework. Nevertheless, there is an increasing interest in point process applications, and methodologies that take nonstationarity into account are welcomed. In this sense, this work proposes an extension of a class of spatial Cox process using spatial deformation. The proposed method enables the deformation behavior to be data-driven, through a multivariate latent Gaussian process. Inference leads to intractable posterior distributions that are approximated via MCMC. The convergence of algorithms based on the Metropolis–Hastings steps proved to be slow, and the computational efficiency of the Bayesian updating scheme was improved by adopting Hamiltonian Monte Carlo (HMC) methods. Our proposal was also compared against an alternative anisotropic formulation. Studies based on synthetic data provided empirical evidence of the benefit brought by the adoption of nonstationarity through our anisotropic structure. A real data application was conducted on the spatial spread of the Spodoptera frugiperda pest in a corn-producing agricultural area in southern Brazil. Once again, the proposed method demonstrated its benefit over alternatives.