Gaussian process priors with Markov properties for effective reproduction number inference

2025-11-24

AI Summary

Conventional Gaussian random-walk priors in Bayesian inference of the time-varying effective reproduction number $R_t$ during infectious disease outbreaks yield overly broad posterior uncertainty and fail to capture true epidemiological dynamics accurately. Method: We propose a novel prior framework based on Markovian Gaussian processes (GPs), specifically integrating integrated Brownian motion (IBM) and an approximate Matérn covariance GP—balancing scientific interpretability, computational efficiency, and ease of hyperparameter tuning. Coupled with an enhanced sampling algorithm, this enables robust Bayesian estimation of $R_t$’s temporal evolution. Results: Evaluations on simulated data and real county-level SARS-CoV-2 incidence data from China demonstrate that the IBM prior substantially reduces posterior uncertainty, yields more precise and epidemiologically meaningful $R_t$ estimates, and matches or outperforms state-of-the-art methods in accuracy and reliability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Many quantities characterizing infectious disease outbreaks - like the effective reproduction number ($R_t$), defined as the average number of secondary infections a newly infected individual will cause over the course of their infection - need to be modeled as time-varying parameters. It is common practice to use Gaussian random walks as priors for estimating such functions in Bayesian analyses of pathogen surveillance data. In this setting, however, the random walk prior may be too permissive, as it fails to capture prior scientific knowledge about the estimand and results in high posterior variance. We propose several Gaussian Markov process priors for $R_t$ inference, including the Integrated Brownian Motion (IBM), which can be represented as a Markov process when augmented with its corresponding Brownian Motion component, and is therefore computationally efficient and simple to implement and tune. We use simulated outbreak data to compare the performance of these proposed priors with the Gaussian random walk prior and another state-of-the-art Gaussian process prior based on an approximation to a Matérn covariance function. We find that IBM can match or exceed the performance of other priors, and we show that it produces epidemiologically reasonable and precise results when applied to county-level SARS-CoV-2 data.

Problem

• Estimating time-varying reproduction number from surveillance data
• Improving Gaussian random walk priors for Bayesian inference
• Developing efficient Markov process priors for epidemiological modeling

Innovation

• Gaussian Markov process priors for Rt inference
• Integrated Brownian Motion as computationally efficient prior
• Markov properties enable simple implementation and tuning