Bayesian modeling for spatial point process with nonstationary covariance structure via spatial deformations

Abstract

Many techniques have been proposed to model space varying observation processes with nonstationary spatial covariance structure and/or anisotropy, usually on a geostatistic framework. Nevertheless, there is an increasing interest in point process applications, and methodologies that take into account nonstationarity are welcomed. In this sense, this work proposes an extension of a class of the well-known spatial Cox process using spatial deformation techniques. The proposed method allows the data to specify, through a latent l-dimensional Gaussian process, what the deformation behavior should be. To perform Bayesian inference Markov Chain Monte Carlo (MCMC) methods are applied. It was necessary to consider the complex relationships between parameters to generate posterior samples. Since traditional algorithms such as Metropolis-Hastings showed slow convergence for the chains, Hamiltonian Monte Carlo (HMC) was applied. Simulations presented the improvement brought by the model that treats anisotropic structures. A real data application is performed on the spatial spreading of the Spodoptera frugiperda pest in an agricultural area of corn production in the South of Brazil and, again,the proposed method presents benefits.