Accelerated inference for stochastic compartmental models with over-dispersed partial observations.

Area of Science:

• Mathematical Biology
• Computational Epidemiology
• Statistical Modeling

Background:

• Partially observed stochastic compartmental models are crucial for understanding disease dynamics.
• Observational over-dispersion presents challenges in accurately estimating model parameters.
• Existing methods, like sequential Monte Carlo, can be computationally intensive.

Purpose of the Study:

• To develop a computationally efficient and accurate approximate likelihood for partially observed stochastic compartmental models.
• To address observational over-dispersion by treating reporting probabilities as latent variables.
• To enable faster and more robust inference for epidemiological models.

Main Methods:

• Derivation of an assumed density approximate likelihood using Laplace approximations within Poisson Approximate Likelihoods (LawPAL).
• Integration of time-varying reporting probabilities as latent variables.
• Asymptotic analysis in the large population regime to establish filtering accuracy.
• Simulation studies to evaluate estimator performance and computational speed.

Main Results:

• The LawPAL method provides a fast, deterministic approximation to the marginal likelihood and filtering distributions.
• The approximation accurately recovers latent disease states and reporting probabilities in the large population limit.
• Maximum approximate likelihood estimation shows favorable performance for ground truth recovery.
• Significant computational speed gains (orders of magnitude) compared to sequential Monte Carlo methods were observed.

Conclusions:

• The developed approximate likelihood offers a computationally efficient alternative for analyzing partially observed stochastic compartmental models.
• The method demonstrates strong performance in recovering key epidemiological parameters and states, particularly in large populations.
• Integration into probabilistic programming languages like Stan facilitates practical Bayesian inference for real-world outbreaks, such as COVID-19 in Switzerland.