部分K函数 (The partial K function)

The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for characterising the interactions between points of one type, or between two different types of points. In this paper, introduce a partial K function, enabling us to account for some of the effects of the other point types when analysing point-point interactions. The partial K function we introduce reduces to the usual K function when the other points are independent of the points of interest and has a similar interpretation. Using examples, we demonstrate how the partial K function can unpick dependence between point types that would otherwise be hidden in the usual K function. We also discuss important bias correction steps and hyperparameter selection. In addition, we discuss an extension to account for other spatial covariates, and demonstrate the methodology on the Lansing Woods dataset.

翻译：K函数及其相关统计量一直是空间点过程分析中的持久工具，为描述单一类型点之间或两种不同类型点之间的相互作用提供了易于计算和解释的汇总统计量。本文引入了一种部分K函数，使得在分析点-点相互作用时能够考虑其他点类型的部分影响。所引入的部分K函数在其他点与目标点独立时退化为常规K函数，并具有类似的解释意义。通过示例，我们展示了部分K函数如何揭示常规K函数中原本隐藏的点类型间依赖关系。文中还讨论了重要的偏差校正步骤与超参数选择方法。此外，我们探讨了扩展该方法以纳入其他空间协变量的方案，并以兰辛森林数据集为例演示了该方法的应用。