Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation

Nguyen-Van-Yen, Benjamin; Moral, Pierre Del; Cazelles, Bernard

doi:10.1016/j.mbs.2021.108583

Cited by 6 publications

(3 citation statements)

References 35 publications

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“…Evaluating the likelihood function for model parameters in finite-population stochastic models involves marginalizing out over the set of all possible configurations of the population amongst the compartments, and the cost of this summation explodes with the number of compartments and the population size. This has prompted development of a variety of simulation-based inference methods based around Data Augmentation MCMC [25,49,48,42,22,47], Approximate Bayesian Computation (ABC) [58,46] and Sequential Monte Carlo (SMC) [6,28,19,38,31]. An attractive feature of the latter two families of methods is that the only way in which the model enters the computational machinery is through simulation: if one can simulate from the model and in the case of ABC quantify the discrepancy between simulated and real data, or in the case of SMC evaluate the likelihood function for an observation model, then in principle, one can apply these methods.…”

Section: Other Inference Algorithms For Stochastic Compartmental Modelsmentioning

confidence: 99%

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

Whitehouse¹,

Whiteley²,

Rimella³

2022

Preprint

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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 the consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results applicable across a broad class of partially observed stochastic compartmental models. Compared to simulation-based methods such as Approximate Bayesian Computation and Sequential Monte Carlo, 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: embedded within Delayed Acceptance Particle Markov Chain Monte Carlo to facilitate Bayesian inference; used to fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; and applied to calibrate a spatial meta-population model of measles.

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Section: Other Inference Algorithms For Stochastic Compartmental Modelsmentioning

confidence: 99%

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

Whitehouse¹,

Whiteley²,

Rimella³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Although there has been significant progress in the area of parameter estimation for stochastic epidemic models (e.g. O'Neill and Roberts, 1999;Kypraios, 2007;Streftaris and Gibson, 2012;Xiang and Neal, 2014;Nguyen-Van-Yen et al, 2021), model assessment methods remain less developed. This paper is concerned with the problem of assessing the fit of stochastic epidemic models, fitted to partially observed temporal outbreak data.…”

Section: Introductionmentioning

confidence: 99%

Posterior Predictive Checking for Partially Observed Stochastic Epidemic Models

2023

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We address the problem of assessing the fit of stochastic epidemic models to data. Two novel model assessment methods are developed, based on disease progression curves, namely the distance method and the position-time method. The methods are illustrated using SIR (susceptible-infective-removed) models. We assume a typical data observation setting in which case-detection times are observed while infection times are not. Both methods involve Bayesian posterior predictive checking, in which the observed data are compared to data generated from the posterior predictive distribution. The distance method does this by calculating distances between disease progression curves, while the position-time method does this pointwise at suitably selected time points. Both methods provide visual and quantitative outputs with meaningful interpretations. The performance of the methods benefits from the development and application of a time-shifting method that accounts for the random time delay until an epidemic takes off. Extensive simulation studies show that both methods can successfully be used to assess the choice of infectious period distribution and the choice of infection rate function.

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“…Data augmentation facilitates Bayesian inference by targeting the joint posterior distribution of the latent epidemic process and SEM parameters. Modern DA algorithms can be more computationally robust than simulation‐based methods, especially in the absence of subject‐level data or when the SEM dynamics are complex (Pooley et al., 2015; Fintzi et al., 2017; Nguyen‐Van‐Yen et al., 2021). However, repeatedly evaluating the MJP likelihood, which is a product of exponential waiting time densities, within a Markov chain Monte Carlo (MCMC) algorithm is prohibitively expensive in large populations.…”

Section: Introductionmentioning

confidence: 99%

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

2021

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Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak transmission dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJP), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is generally impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulationbased computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that replaces the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings. Existing LNA frameworks are inappropriate for incidence data and depend on simulation-based methods or an assumption that disease counts are normally distributed. We demonstrate how to reparameterize a SEM to properly analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and can be applied to a broad class of SEMs. We apply our method to national-level surveillance counts from the 2013-2015 West Africa Ebola outbreak, modeling within-country transmission and importation of infections from neighboring countries.

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Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation

Cited by 6 publications

References 35 publications

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

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

Posterior Predictive Checking for Partially Observed Stochastic Epidemic Models

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

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