Spatiotemporal nonhomogeneous poisson model with a seasonal component applied to the analysis of extreme rainfall

This paper develops an extension of spatiotemporal models that handle count data using nonhomogeneous Poisson processes. In this new proposal, we incorporate a seasonal cycle component in the definition of the intensity function to control possible effects produced by the occurrence of the event of interest in regular periods. The seasonal cycle can cause problems in estimating the shape parameter of the Weibull and generalized Goel intensity functions. This shape parameter serves to confront the research hypothesis that seeks to identify a trend in the occurrence rate of an event of interest. In the case of the Weibull intensity function, a value significantly equal to one of the shape parameters indicates a constant rate of occurrence, less than one indicates a decreasing rate, and greater than one indicates an increasing rate. In the case of the Goel intensity function, parameter values less than or equal to one indicate a decreasing occurrence rate, and values greater than one indicate the presence of a change point. We also built a spatial model using the Musa-Okumoto intensity function as an alternative to approximate counting processes for which there is a decreasing trend in the occurrence rate of the event of interest. We estimated the parameters of the proposed method from a Bayesian perspective. Finally, we fitted the proposed model and compared it with other approximations to analyze the frequency of extreme rainfall in the northern region of the states of Maranhão and Piauí in northeastern Brazil over ten years. Among the main results, we found that (1) the proposed method has proven superior in terms of fit and prediction performance than the other models, and (2) unlike other approximations, the proposed model does not detect changes in the rate of extreme rainfall occurrences.

本研究提出了一种采用非齐次泊松过程（nonhomogeneous Poisson processes）处理计数数据（count data）的时空模型（spatiotemporal models）扩展方法。在该扩展模型中，我们在强度函数（intensity function）的定义中纳入季节周期分量（seasonal cycle component），用以管控目标事件在周期性发生时所引发的潜在效应。季节周期因素可能会对威布尔（Weibull）强度函数与广义Goel强度函数（generalized Goel intensity function）的形状参数（shape parameter）估计造成干扰。上述形状参数可用于检验旨在识别目标事件发生频率趋势的研究假设。针对威布尔强度函数而言，若其形状参数显著等于1，则代表事件发生频率恒定；若形状参数小于1，则发生频率呈下降趋势；若大于1，则发生频率呈上升趋势。针对Goel强度函数而言，若参数值小于或等于1，则发生频率呈下降趋势；若参数值大于1，则代表存在变点（change point）。此外，我们还构建了一款基于Musa-Okumoto强度函数（Musa-Okumoto intensity function）的空间模型，作为近似处理目标事件发生频率呈下降趋势的计数过程的替代方案。我们从贝叶斯视角（Bayesian perspective）对所提方法的参数进行了估计。最后，我们将所提模型与其他近似方法进行拟合对比，用以分析巴西东北部马拉尼昂州（Maranhão）与皮奥伊州（Piauí）北部地区近十年的极端降雨（extreme rainfall）发生频率。主要研究结果显示：其一，所提方法在拟合效果与预测性能上均优于其他模型；其二，与其他近似方法不同，所提模型未检测到极端降雨发生频率的变化。