Deep Simulation-Based Inference for Inhomogeneous Bivariate Log-Gaussian Cox Processes

2026-07-14

AI Summary

This study addresses the challenges of high-dimensional parameter estimation and the difficulty of specifying broad prior ranges in inhomogeneous bivariate log-Gaussian Cox processes when covariates are present. To overcome these issues, the authors propose a two-stage decoupled estimation framework: first, classical Poisson regression is employed to estimate first-order intensity parameters; subsequently, simulation-based inference combined with deep neural networks is used to learn latent field parameters. Innovatively, spatial point patterns are transformed into two-dimensional image inputs, enabling the network to directly capture complex spatial structures. This approach effectively circumvents the traditional reliance of simulation-based inference on expansive parameter spaces, achieving high-precision latent field estimation in simulation studies and demonstrating practical utility through application to gorilla distribution data.

Abstract

We propose a computationally efficient simulation-based estimation method with a two-step procedure for inhomogeneous bivariate Log-Gaussian Cox Processes. It combines classical Poisson estimation for the first-order parameters with simulation-based inference using neural networks for the latent field parameters. By separating the estimations, it reduces the complexity of high dimensional parameter estimation and the need for the simulation-based method to specify broad parameter ranges in the presence of covariates. In addition, we introduce two dimensional image inputs that enable the model to learn spatial information directly. Simulation results demonstrate that the proposed approach provides accurate estimates of the latent field parameters. We further illustrate the method's practical applicability using the gorilla dataset.

Problem

• Log-Gaussian Cox Processes
• simulation-based inference
• inhomogeneous bivariate
• parameter estimation
• spatial information

Innovation

• simulation-based inference
• bivariate Log-Gaussian Cox process
• neural networks
• two-step estimation
• spatial image input