Neural Posterior Estimation for Spatial Individual-Level Epidemic Models

2026-05-27

AI Summary

This work addresses the computational challenges of Bayesian inference in spatial individual-level epidemic models, which traditionally rely on Markov chain Monte Carlo (MCMC) methods that are costly and poorly scalable. For the first time, the authors introduce neural posterior estimation (NPE) to this domain, employing conditional normalizing flows parameterized by graph neural networks (GNNs) and convolutional neural networks (CNNs), trained on simulated data to directly approximate the posterior distribution and enable amortized inference. The proposed approach effectively integrates individual infection states with spatial location information, yielding well-calibrated posteriors under fully observed, randomly missing, and partially observed data scenarios. Experiments on the 2001 UK foot-and-mouth disease outbreak demonstrate that GNN-NPE achieves substantial speedups over MCMC while maintaining reliable uncertainty quantification.

Abstract

Spatial individual-level models (ILMs) provide a flexible framework for modelling infectious disease transmission across populations with known locations. Bayesian inference for these models relies on Markov chain Monte Carlo (MCMC), which requires repeated likelihood evaluation and, when parts of the epidemic trajectory are unobserved, data-augmented sampling over high-dimensional latent variables. This computational cost limits the applicability of MCMC to large populations and to settings requiring inference across multiple outbreaks. We propose using neural posterior estimation (NPE) for amortised Bayesian inference in spatial ILMs. NPE trains a conditional normalising flow on simulated data to approximate the posterior directly, bypassing likelihood evaluation at inference time. We compare two embedding architectures: a convolutional neural network (CNN) operating on the population-level incidence curve and a graph neural network (GNN) operating on individual-level infection and location data. In a simulation study under full observation, stochastic removals, and partial observation, both variants produce well-calibrated posteriors, with the GNN embedding yielding lower error and narrower credible intervals for the spatial transmission parameters. We apply the framework to a spatial SEIR model on 1,177 farm locations from the 2001 UK foot-and-mouth disease outbreak. GNN-NPE maintains calibrated coverage and is substantially faster than MCMC on a per-epidemic basis.

Problem

• spatial individual-level models
• Bayesian inference
• Markov chain Monte Carlo
• computational cost
• epidemic trajectory

Innovation

• Neural Posterior Estimation
• Spatial Individual-Level Models
• Graph Neural Network
• Amortised Bayesian Inference
• Normalising Flow