Nonparametric inference for nonstationary spatial point processes

TL;DR

This paper introduces a nonparametric Bayesian model for nonstationary spatial point processes that captures complex spatial features like abrupt changes and hotspots, using a partitioned Gaussian process framework with exact inference.

Contribution

It proposes a novel spatial Cox process model with a random partition approach and a discretization-free MCMC algorithm for efficient, exact inference of nonstationary spatial point patterns.

Findings

Successfully captures sharp intensity transitions and hotspots.

Reduces computational complexity compared to traditional Gaussian process models.

Demonstrates effectiveness on synthetic and real-world data.

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.