binspp: An R Package for Bayesian Inference for Neyman-Scott Point Processes with Complex Inhomogeneity Structure

TL;DR

This paper introduces the binspp R package, enabling Bayesian MCMC inference for complex Neyman-Scott point process models with inhomogeneity and dispersion variations, providing accurate estimates and comprehensive diagnostics.

Contribution

The paper presents a novel Bayesian MCMC approach and an R package for inference on complex Neyman-Scott point processes with inhomogeneity and dispersion modeling.

Findings

Provides accurate Bayesian estimates for complex models.

Includes detailed graphical diagnostics and spatial covariate modeling.

Extends Neyman-Scott processes to overdispersed/underdispersed clusters.

Abstract

The Neyman-Scott point process is a widely used point process model which is easily interpretable and easily extendable to include various types of inhomogeneity. The inference for such complex models is then complicated and fast methods, such as minimum contrast method or composite likelihood approach do not provide accurate estimates or fail completely. Therefore, we introduce Bayesian MCMC approach for the inference of Neymann-Scott point process models with inhomogeneity in any or all of the following model components: process of cluster centers, mean number of points in a cluster, spread of the clusters. We also extend the Neyman-Scott point process to the case of overdispersed or underdispersed cluster sizes and provide a Bayesian MCMC algorithm for its inference. The R package binspp provides these estimation methods in an easy to handle implementation, with detailed graphical output including traceplots for all model parameters and further diagnostic plots. All inhomogeneities are modelled by spatial covariates and the Bayesian inference for the corresponding regression parameters is provided.