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

2025/05/11 by Michael Whitehouse, Whitehouse, Michael
Mathematics · #COVID-19 epidemiological studies #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2505.06935

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An assumed density approximate likelihood is derived for a class of partially observed stochastic compartmental models which permit observational over-dispersion. This is achieved by treating time-varying reporting probabilities as latent variables and integrating them out using Laplace approximations within Poisson Approximate Likelihoods (LawPAL), resulting in a fast deterministic approximation to the marginal likelihood and filtering distributions. We derive an asymptotically exact filtering result in the large population regime, demonstrating the approximation's ability to recover latent disease states and reporting probabilities. Through simulations we: 1) demonstrate favorable behavior of the maximum approximate likelihood estimator in the large population and time horizon regime in terms of ground truth recovery; 2) demonstrate order of magnitude computational speed gains over a sequential Monte Carlo likelihood based approach, and explore the statistical compromises our approximation implicitly makes. We conclude by embedding our methodology within the probabilistic programming language Stan for automated Bayesian inference to develop a model of practical interest using data from the Covid-19 outbreak in Switzerland.

Citations

• Accelerating Bayesian inference for stochastic epidemic models using incidence data
• The Lifebelt Particle Filter for robust estimation from low-valued count data
• Approximating optimal SMC proposal distributions in individual-based epidemic models
• Systemic Infinitesimal Over-dispersion on Graphical Dynamic Models
• Inference in Stochastic Epidemic Models via Multinomial Approximations
• Bayesian workflow for disease transmission modeling in Stan
• Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation
• Early dynamics of transmission and control of COVID-19: a mathematical modelling study
• Inference for stochastic kinetic models from multiple data sources for joint estimation of infection dynamics from aggregate reports and virological data
• Efficient data augmentation for fitting stochastic epidemic models to\n prevalence data
• Predictive Modeling of Cholera Outbreaks in Bangladesh
• Can local particle filters beat the curse of dimensionality?
• A Widely Applicable Bayesian Information Criterion
• Applications of Mathematics to Medical Problems

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