Bayesian inference for Neyman-Scott point processes with anisotropic clusters

2025/05/14 by Dvořák, Jiří, Ewers, Emily, Mrkvička, Tomáš +1
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2505.09786

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.

Citations

• Nonparametric Isotropy Test for Spatial Point Processes using Random Rotations
• binspp: An R Package for Bayesian Inference for Neyman-Scott Point Processes with Complex Inhomogeneity Structure
• A review on anisotropy analysis of spatial point patterns
• Extremal Depth for Functional Data and Applications

Related

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