Divide-and-Conquer Neural Bayes Estimation for Spatial and Spatiotemporal Point Process Models

Abstract

Spatial and spatiotemporal point process models are widely used to analyze event data across many scientific disciplines, but likelihood-based Bayesian inference is often computationally prohibitive due to intractable likelihoods, high-dimensional latent structures, and dependence on event history. Existing approximate and likelihood-free methods mitigate some of these challenges, but often at the cost of reduced statistical efficiency, imperfect uncertainty quantification, or information loss from reliance on predefined summary statistics. A promising recent approach involves neural networks, but it has only been explored in purely spatial or temporal settings and requires a computationally expensive training stage for large domains or dense point patterns. Here, we propose a divide-and-conquer neural Bayes estimation framework for spatial and spatiotemporal point process models. Our method operates directly on raw point pattern realizations using transformer-based architectures on partitions of the spatiotemporal domain, together with an attention mechanism to optimally combine locally extracted summaries. Simulation studies demonstrate reliable inference with improved scalability relative to existing general-purpose neural inference approaches and classical likelihood-based methods. We further demonstrate the practical applicability of our approach through an analysis of whale call data in Cape Cod Bay, MA, where, once trained, the estimator yields parameter estimates and credible intervals at negligible computational cost.