Advances in approximate Bayesian inference for models in epidemiology

Abstract

Bayesian inference methods are useful in infectious diseases modelling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter inference through assimilation of observational data in these models remains challenging. While asymptotically exact Bayesian methods offer theoretical guarantees for accurate inference, they can be computationally demanding and impractical for real-time outbreak analysis. This review synthesizes recent advances in approximate Bayesian inference methods that aim to balance inferential accuracy with scalability. We focus on four prominent families: Approximate Bayesian Computation, Bayesian Synthetic Likelihood, Integrated Nested Laplace Approximation, and Variational Inference. For each method, we evaluate its relevance to epidemiological applications, emphasizing innovations that improve both computational efficiency and inference accuracy. We also offer practical guidance on method selection across a range of modelling scenarios. Finally, we identify hybrid exact approximate inference as a promising frontier that combines methodological rigor with the scalability needed for the response to outbreaks. This review provides epidemiologists with a conceptual framework to navigate the trade-off between statistical accuracy and computational feasibility in contemporary disease modelling. • Fitting epidemiological models is challenging when real-time updates are required. • Review the main four families of approximate Bayesian methods: ABC, BSL, INLA, and VI. • Summarize recent developments and areas of active research in these fields. • Propose a decision-making scheme for practitioners to choose the most suitable tool. • Conclude by identifying exciting research frontiers that arise from this synthesis.

Topics & Concepts