Bognar Matthew A
University of Iowa, Department of Statistics and Actuarial Science, 241 Schaeffer Hall, Iowa City, Iowa, 52242, USA.
Biom J. 2006 Apr;48(2):205-19. doi: 10.1002/bimj.200410166.
The K function is a summary of spatial dependence in spatial point processes. In practice one observes a realization of the spatial point process, called a spatial point pattern. Although the K function of a spatial point process is typically unknown, several estimators of the process K function have been put forth. These estimators, however, are based upon empirical averages; the complicated distributional properties of the estimators unfortunately complicates interval estimation. In this paper, we propose a Bayesian inferential framework, allowing inference for the K function of the spatial point process (including interval estimation). Of particular interest is the unique use of the posterior predictive distribution to (efficiently) enable such inferences. To demonstrate our technique, the well known Swedish pine sapling data (Strand, 1972) is analyzed, including a discussion on evaluating model fit.
K函数是空间点过程中空间依赖性的一种总结。在实际中，人们会观察到空间点过程的一个实现，称为空间点模式。虽然空间点过程的K函数通常是未知的，但已经提出了几种该过程K函数的估计量。然而，这些估计量是基于经验平均值的；不幸的是，估计量复杂的分布特性使得区间估计变得复杂。在本文中，我们提出了一个贝叶斯推断框架，用于对空间点过程的K函数进行推断（包括区间估计）。特别有趣的是后验预测分布的独特使用（有效地）实现了此类推断。为了展示我们的技术，我们分析了著名的瑞典松树幼苗数据（斯特兰德，1972年），包括对评估模型拟合的讨论。
