Bayesian nonparametric estimation of pair correlation function for inhomogeneous spatial point processes

Abstract

The pair correlation function (PCF) is a useful tool for studying spatial point patterns. It is often estimated by some nonparametric approach such as kernel smoothing. However, the statistical properties of the kernel estimator are highly dependent on the choice of bandwidth. An inappropriate value of the bandwidth may lead to an estimator with a large bias or variance or both. In this work, we present an alternative PCF estimator based on Bayesian nonparametric regression. The method provides data-driven smoothing and intuitive uncertainty measures, together with efficient computation. The merits of our method are demonstrated via a simulation study and a couple of applications involving astronomy data and data on restaurant locations.

Keywords:

• Bayesian smoothing
• inhomogeneous spatial point processes
• integrated nested Laplace approximation
• pair correlation function