arXiv subjects

Michael Whitehouse

Publications and source records attributed to Michael Whitehouse.

3 recordsLinked to original sources

arXiv2025

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

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.

stat.ME↗

arXiv2025

Scalable calibration of individual-based epidemic models through categorical approximations

Traditional compartmental models capture population-level dynamics but fail to characterize individual-level risk. The computational cost of exact likelihood evaluation for partially observed individual-based models, however, grows exponentially with the population size, necessitating approximate inference. Existing sampling-based methods usually require multiple simulations of the individuals in the population and rely on bespoke proposal distributions or summary statistics. We propose a deterministic approach to approximating the likelihood using categorical distributions. The approximate likelihood is amenable to automatic differentiation so that parameters can be estimated by maximization or posterior sampling using standard software libraries such as Stan or TensorFlow with little user effort. We prove the consistency of the maximum approximate likelihood estimator. We empirically test our approach on several classes of individual-based models for epidemiology: different sets of disease states, individual-specific transition rates, spatial interactions, under-reporting and misreporting. We demonstrate ground truth recovery and comparable marginal log-likelihood values at substantially reduced cost compared to competitor methods. Finally, we show the scalability and effectiveness of our approach with a real-world application on the 2001 UK Foot-and-Mouth outbreak, where the simplicity of the CAL allows us to include 162775 farms.

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arXiv2023

Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods

Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large population limit drives consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results which apply to a broad class of partially observed stochastic compartmental models and address the large population limit. PALs are simple to implement, involving only elementary arithmetic operations and no tuning parameters, and fast to evaluate, requiring no simulation from the model and having computational cost independent of population size. Through examples we demonstrate how PALs can be used to: fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; compare over-dispersion mechanisms in a model of rotavirus by embedding PALs within sequential Monte Carlo; and evaluate the role of unit-specific parameters in a meta-population model of measles.

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