Spatial and spatiotemporal point process models are widely used across scientific disciplines, but their likelihood-based Bayesian inference often becomes 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 issues, yet they typically sacrifice statistical efficiency, produce imperfect uncertainty quantification, or rely on predefined summary statistics that can discard information.
The proposed divide-and-conquer neural Bayes estimation framework addresses these limitations by partitioning the spatiotemporal domain and applying transformer-based architectures directly to raw point pattern realizations. An attention mechanism then optimally combines locally extracted summaries, eliminating the need for hand-crafted summary statistics and reducing the computational burden of training on large domains or dense point patterns.
Simulation studies show that the method delivers reliable inference with improved scalability relative to both general-purpose neural inference approaches and classical likelihood-based methods. The authors further demonstrate practical applicability on whale call data from Cape Cod Bay, MA, where the trained estimator produces parameter estimates and credible intervals at negligible computational cost.