Gaussian approximations for fast Bayesian inference of partially observed branching processes with applications to epidemiology

2025-11-27

AI Summary

Bayesian inference of states and parameters for continuous-time multitype branching processes—such as epidemic transmission models—under partial observation is computationally prohibitive with conventional sequential Monte Carlo methods, especially during exponential population growth or over long time horizons. Method: This paper proposes a fast Bayesian inference framework based on Gaussian approximation. It replaces nonparametric particle filtering with an analytical Gaussian approximation, decoupling computational complexity from population size. The method integrates Kalman filtering with a hybrid strategy to balance efficiency for large populations and accuracy for small ones. Contribution/Results: Experiments demonstrate that the approach closely approximates true posteriors in both simple and complex epidemic models, achieving substantial speedups. It successfully scales to real-world COVID-19 data with time-varying parameters, overcoming the scalability limitations of exact inference methods.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Probabilistic Inference
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo, can be computationally challenging when the populations that are being modelled grow exponentially or the time series is long. Instead, we derive a Gaussian approximation for the transition function of the process that leads to a Kalman filtering algorithm that runs in a time independent of the population sizes. We also develop a hybrid approach for when populations are smaller and the approximation is less applicable. We investigate the performance of our approximation and algorithms to both a simple and a complex epidemic model, finding good adherence to the true posterior distributions in both cases with large computational speed-ups in most cases. We also apply our method to a COVID-19 dataset with time dependent parameters where exact methods are intractable due to the population sizes involved.

Problem

• Develops Gaussian approximation for fast Bayesian inference of branching processes
• Enables Kalman filtering independent of population size for computational efficiency
• Applies method to epidemic models and COVID-19 data with time-dependent parameters

Innovation

• Gaussian approximation for branching process transitions
• Kalman filtering independent of population size
• Hybrid approach for small population scenarios