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.

中文翻译：

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具有空间变形的非均匀泊松过程地统计模型

在本文中，我们提出了使用非均匀泊松模型进行计数过程的地统计模型。这项工作旨在将强度函数建模为两个部分的总和：空间和时间。使用高斯过程对空间分量进行建模，其中协方差结构被假定为各向异性。通过应用空间变形方法可以纳入各向异性。对时间成分进行建模，以使其有关时间的行为具有Goel过程的结构。提出的模型的推论是从贝叶斯角度获得的。使用马尔可夫链蒙特卡罗方法获得参数估计。根据在Maranhão和Piauí各州分布的29个监测站的降雨降水量，将提出的模型调整为一组实际数据。从1980年1月1日至2010年12月31日，是巴西东北部地区的第31年。目的是估计超过一定阈值的降雨频率。