Nonparametric inference for nonstationary spatial point processes

2025-07-23

AI Summary

Traditional models struggle to characterize nonstationary spatial point processes—e.g., those exhibiting intensity discontinuities, hotspots, or spatial heterogeneity. To address this, we propose a Cox process model based on stochastic spatial partitioning. Our method employs a partitioned Gaussian process prior to explicitly capture intensity discontinuities and local variations; integrates a random segmentation mechanism with infinite-dimensional MCMC sampling to avoid grid-based discretization, thereby preserving nonparametric flexibility while substantially reducing computational cost; and incorporates spatial covariates to elucidate underlying drivers of intensity variation. Experiments on synthetic and real-world datasets demonstrate that the approach achieves high-fidelity inference of nonstationary intensity structures, robustly identifies change-point boundaries and hotspot regions, and provides a scalable, interpretable nonparametric Bayesian framework for complex spatial point patterns.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying intensity function -- features that are difficult to capture with standard modeling approaches. This paper proposes a spatial Cox process model in which nonstationarity is induced through a random partition of the spatial domain, with conditionally independent Gaussian process priors specified across the resulting regions. This construction allows for heterogeneous spatial behavior, including sharp transitions in intensity. To ensure exact inference, a discretization-free MCMC algorithm is developed to target the infinite-dimensional posterior distribution without approximation. The random partition framework also reduces the computational burden typically associated with Gaussian process models. Spatial covariates can be incorporated to account for structured variation in intensity. The proposed methodology is evaluated through synthetic examples and real-world applications, demonstrating its ability to flexibly capture complex spatial structures. The paper concludes with a discussion of potential extensions and directions for future work.

Problem

• Modeling nonstationary spatial point processes with abrupt changes
• Capturing spatially varying intensity without standard approaches
• Reducing computational burden in Gaussian process models

Innovation

• Random partition induces nonstationarity in Cox process
• Discretization-free MCMC for exact infinite-dimensional inference
• Conditionally independent Gaussian process priors per region