Second-order statistics play a crucial role in analysing point processes. Previous research has specifically explored locally weighted second-order statistics for point processes, offering diagnostic tests in various spatial domains. However, there remains a need to improve inference for complex intensity functions, especially when the point process likelihood is intractable and in the presence of interactions among points. This paper addresses this gap by proposing a method that exploits local second-order characteristics to account for local dependencies in the fitting procedure. Our approach utilises the Papangelou conditional intensity function for general Gibbs processes, avoiding explicit assumptions about the degree of interaction and homogeneity. We provide simulation results and an application to real data to assess the proposed method's goodness-of-fit. Overall, this work contributes to advancing statistical techniques for point process analysis in the presence of spatial interactions.

翻译：二阶统计量在分析点过程中起着关键作用。已有研究专门探讨了点过程在局部加权二阶统计量中的应用，为不同空间领域的诊断检验提供了支持。然而，当点过程似然函数难以处理且存在点间交互作用时，针对复杂强度函数的推断仍有改进空间。本文通过提出一种利用局部二阶特征来拟合过程中局部依赖关系的方法，填补了这一研究空白。该方法采用通用吉布斯过程的Papangelou条件强度函数，避免了对交互程度和同质性做出显式假设。我们提供了模拟结果及真实数据应用案例，以评估所提方法的拟合优度。总体而言，本研究为存在空间交互作用时点过程分析的统计方法发展做出了贡献。