On Bayesian inference for the K function.

Abstract

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.