Bayesian inference for Neyman-Scott point processes with anisotropic clusters

TL;DR

This paper introduces a Bayesian MCMC method for Neyman-Scott point processes that models covariate-dependent anisotropy and inhomogeneity, enabling detailed inference and hypothesis testing.

Contribution

It extends Bayesian inference techniques to handle anisotropic and inhomogeneous cluster processes, providing new tools for parameter estimation and hypothesis testing.

Findings

Successful simulation study demonstrating method effectiveness

Credible intervals for covariates and anisotropy parameters

Hypothesis tests for cluster orientation and elongation

Abstract

There are few inference methods available to accommodate covariate-dependent anisotropy in point process models. To address this, we propose an extended Bayesian MCMC approach for Neyman-Scott cluster processes. We focus on anisotropy and inhomogeneity in the offspring distribution. Our approach provides parameter estimates as well as significance tests for the covariates and anisotropy through credible intervals, which are determined by the posterior distributions. Additionally, it is possible to test the hypothesis of constant orientation of clusters or constant elongation of clusters. We demonstrate the applicability of this approach through a simulation study for a Thomas-type cluster process.