A multi-stage Bayesian approach to fit spatial point process models

TL;DR

The paper tackles the computational bottleneck of exact Bayesian inference for spatial point process models by introducing a flexible multi-stage recursive Bayes framework (PPRB) that partitions the inference into a tractable first stage (often via logistic regression approximations) and a second stage that corrects with the complete likelihood, enabled by parallel computation of the intractable integral Λ(𝒮). It presents two practical first-stage strategies (GLM-A and GLM-E) and demonstrates substantial speedups over single-stage MCMC, while preserving accurate posterior inference for parameters and derived quantities such as total abundance. The authors extend the approach to compact observation windows and incorporate neural-network basis expansions to capture complex spatial heterogeneity, applying the method to harbor seal pup data in Johns Hopkins Inlet and validating with simulation studies. The framework yields exact Bayesian inference for IPP under the complete likelihood, scales with cores, and supports predictive analytics outside observation windows, which is valuable for ecological monitoring and spatial risk assessment.

Abstract

Spatial point process (SPP) models are commonly used to analyze point pattern data in many fields, including presence-only data in ecology. Existing exact Bayesian methods for fitting these models are computationally expensive because they require approximating an intractable integral each time parameters are updated and often involve algorithm supervision (i.e., tuning in the Bayesian setting). We propose a flexible, efficient, and exact multi-stage recursive Bayesian approach to fitting SPP models that leverages parallel computing resources to obtain realizations from the joint posterior, which can then be used to obtain inference on derived quantities. We outline potential extensions, including a framework for analyzing study designs with compact observation windows and a neural network basis expansion for increased model flexibility. We demonstrate this approach and its extensions using a simulation study and analyze data from aerial imagery surveys to improve our understanding of spatially explicit abundance of harbor seal (Phoca vitulina) pups in Johns Hopkins Inlet, a protected tidewater glacial fjord in Glacier Bay National Park, Alaska.

Figures (24)

• Figure 1: Flowchart of multi-stage algorithm with various first-stage sampling strategies (PG, HMC, GLM-A, GLM-E).
• Figure 2: (a) Intensity heat map for simulated data. (b) Realization of simulated points. Points located within the compact windows (red; $n$ = 580) were used to fit the model.
• Figure 3: Comparison of marginal posterior 95% credible intervals for the single-stage method and various multi-stage methods. The true values of the parameters are shown in dashed gray.
• Figure 4: Comparison of bivariate joint posterior distributions for each pair of model parameters. Contours represent kernel density estimates of the joint posterior distributions. The GLM-E contours (pink) are overlaid on top of the single-stage contours (gray).
• Figure 5: Posterior predictive distribution for $N$ using posterior realizations obtained using the GLM-E method. The true value of $N$ is marked in dashed red.