Technology Category
Machine Learning: Kernel MethodsReasoning under Uncertainty: Relational Probabilistic ModelsData Mining & Knowledge Management: Anomaly/Outlier Detection
Bayesian inference for Neyman-Scott point processes with anisotropic clusters
🤖 AI Summary
This paper addresses the joint inference of covariate-dependent anisotropy and nonstationarity in Neyman–Scott point process modeling—a longstanding challenge. We propose the first Bayesian MCMC inference framework specifically targeting offspring distributions. Methodologically, we introduce a covariate-driven anisotropic kernel parameterized by direction and stretch, integrated with adaptive Metropolis–Hastings sampling and posterior credible interval analysis. This enables interpretable estimation of anisotropy parameters and Bayesian significance testing for directional or stretch constancy in Thomas-type clustering processes. Simulation studies demonstrate that our approach accurately detects covariate modulation of anisotropy, substantially enhancing model flexibility, statistical reliability, and mechanistic interpretability in spatial cluster structure modeling.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Inference methods for covariate-dependent anisotropy in point processes
Bayesian MCMC approach for Neyman-Scott cluster processes
Testing anisotropy and inhomogeneity in offspring distribution
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extended Bayesian MCMC for Neyman-Scott processes
Handles covariate-dependent anisotropy and inhomogeneity
Provides parameter estimates and significance tests
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