A non-homogeneous Poisson process geostatistical model with spatial deformation

In this paper, we propose a geostatistical model for the counting process using a non-homogeneous Poisson model. This work aims to model the intensity function as the sum of two components: spatial and temporal. The spatial component is modeled using a Gaussian process in which the covariance structure is assumed to be anisotropic. Anisotropy is incorporated by applying a spatial deformation approach. The temporal component is modeled in such a way that its behavior concerning time has the structure of a Goel process. The inferences for the proposed model are obtained from a Bayesian perspective. The parameter estimation is obtained using Markov Chain Monte Carlo methods. The proposed model is adjusted to a set of real data, referring to the rain precipitation in 29 monitoring stations, distributed in the states of Maranhão and Piauí, in the northeast region of Brazil, in 31 years, from 01/01/1980 to 12/31/2010. The objective is to estimate the frequency of rain that exceeded a certain threshold.