Cloud-to-ground lightning strikes observed in a specific geographical domain over time can be naturally modeled by a spatio-temporal point process. Our focus lies in the parametric estimation of its intensity function, incorporating both spatial factors (such as altitude) and spatio-temporal covariates (such as field temperature, precipitation, etc.). The events are observed in France over a span of three years. Spatio-temporal covariates are observed with resolution $0.1^\circ \times 0.1^\circ$ ($\approx 100$km$^2$) and six-hour periods. This results in an extensive dataset, further characterized by a significant excess of zeroes (i.e., spatio-temporal cells with no observed events). We reexamine composite likelihood methods commonly employed for spatial point processes, especially in situations where covariates are piecewise constant. Additionally, we extend these methods to account for zero-deflated subsampling, a strategy involving dependent subsampling, with a focus on selecting more cells in regions where events are observed. A simulation study is conducted to illustrate these novel methodologies, followed by their application to the dataset of lightning strikes.

翻译：我国特定地理区域内随时间观测到的云地闪电可自然建模为时空点过程。本文重点研究其强度函数的参数估计，同时纳入空间因子（如海拔）与时空协变量（如地表温度、降水量等）。观测数据覆盖法国三年期间，时空协变量分辨率达 0.1°×0.1°（约100平方公里）及六小时时段，由此形成大规模数据集，且呈现显著零膨胀特征（即无事件观测的时空单元占比极高）。我们重新审视了空间点过程中常用的复合似然方法，尤其适用于协变量分段常量的场景；同时扩展这些方法以纳入零膨胀子抽样策略——该策略涉及依赖性子抽样，侧重在事件发生区域选取更多单元。通过仿真实验验证新方法，进而将其应用于闪电数据集。