Advances in approximate Bayesian inference for models in epidemiology.

Area of Science:

• Epidemiology
• Computational Biology
• Biostatistics

Background:

• Bayesian inference is crucial for infectious disease modeling, enabling uncertainty propagation and handling complex data.
• Exact Bayesian methods are computationally intensive, limiting their use in real-time outbreak analysis.
• Challenges remain in parameter inference for epidemiological models using observational data.

Purpose of the Study:

• To review recent advances in approximate Bayesian inference methods for infectious disease modeling.
• To evaluate the scalability and accuracy of these methods for epidemiological applications.
• To provide practical guidance for selecting appropriate Bayesian inference techniques.

Main Methods:

• Focus on four families of approximate Bayesian inference: Approximate Bayesian Computation (ABC), Bayesian Synthetic Likelihood (BSL), Integrated Nested Laplace Approximation (INLA), and Variational Inference (VI).
• Review innovations enhancing computational efficiency and inference accuracy in these methods.
• Discuss hybrid exact approximate inference approaches.

Main Results:

• Approximate Bayesian methods offer a balance between inferential accuracy and computational scalability.
• Specific methods like ABC, BSL, INLA, and VI show promise for epidemiological applications.
• Hybrid methods represent a frontier for rigorous yet scalable inference.

Conclusions:

• Approximate Bayesian inference methods are essential for modern, data-driven infectious disease modeling.
• Method selection depends on balancing statistical rigor with computational feasibility for outbreak response.
• Further research into hybrid methods can bridge the gap between accuracy and scalability.