Bayesian inference for stochastic epidemics in closed populations

Streftaris, George; Gibson, Gavin J.

doi:10.1191/1471082x04st065oa

Cited by 66 publications

(56 citation statements)

References 11 publications

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“…For example, choices of temporal distributions influence both epidemic final size and the persistence of disease, and have important implications for devising effective control strategies which target symptomatic subjects and the timing of infectiousness [6,12,13]. There are examples of such effects related to the parametric form of incubation and infectious period distributions in models of measles Figure 7.…”

Section: Discussionmentioning

confidence: 99%

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New model diagnostics for spatio-temporal systems in epidemiology and ecology

Lau

Marion

Streftaris³

et al. 2014

J. R. Soc. Interface.

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A cardinal challenge in epidemiological and ecological modelling is to develop effective and easily deployed tools for model assessment. The availability of such methods would greatly improve understanding, prediction and management of disease and ecosystems. Conventional Bayesian model assessment tools such as Bayes factors and the deviance information criterion (DIC) are natural candidates but suffer from important limitations because of their sensitivity and complexity. Posterior predictive checks, which use summary statistics of the observed process simulated from competing models, can provide a measure of model fit but appropriate statistics can be difficult to identify. Here, we develop a novel approach for diagnosing mis-specifications of a general spatio-temporal transmission model by embedding classical ideas within a Bayesian analysis. Specifically, by proposing suitably designed non-centred parametrization schemes, we construct latent residuals whose sampling properties are known given the model specification and which can be used to measure overall fit and to elicit evidence of the nature of misspecifications of spatial and temporal processes included in the model. This model assessment approach can readily be implemented as an addendum to standard estimation algorithms for sampling from the posterior distributions, for example Markov chain Monte Carlo. The proposed methodology is first tested using simulated data and subsequently applied to data describing the spread of Heracleum mantegazzianum (giant hogweed) across Great Britain over a 30-year period. The proposed methods are compared with alternative techniques including posterior predictive checking and the DIC. Results show that the proposed diagnostic tools are effective in assessing competing stochastic spatio-temporal transmission models and may offer improvements in power to detect model mis-specifications. Moreover, the latent-residual framework introduced here extends readily to a broad range of ecological and epidemiological models.

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Section: Discussionmentioning

confidence: 99%

“…rsif.royalsocietypublishing.org J. R. Soc. Interface 11: 20131093 [9][10][11], smallpox [12] and AIDS [13]. It is well known that the spatial transmission mechanisms are difficult to assess in practice yet have major implications for optimal control strategies.…”

Section: Discussionmentioning

confidence: 99%

New model diagnostics for spatio-temporal systems in epidemiology and ecology

Lau

Marion

Streftaris³

et al. 2014

J. R. Soc. Interface.

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“…Also, the exponential distribution has been widely used to describe sojourn times in various compartments in the study of epidemics, partly owing to its mathematically convenient Markov property, as for example in the general susceptible-infectious-removed epidemic model (Bailey 1975). In this paper, following the work in Streftaris & Gibson (2004), we employ the two-parameter Weibull(, ) distribution with probability density…”

Section: Model and Methodologymentioning

confidence: 99%

“…Gelfand & Smith 1990;Tierney 1994), which offers tools for stochastic integration in problems of increased complexity and dimension. A single-component Metropolis-Hastings algorithm is used, in a manner similar to that described in Streftaris & Gibson (2004). Details of the algorithm implementation are given in electronic Appendix A.…”

Section: (B) Bayesian Inferencementioning

confidence: 99%

Bayesian analysis of experimental epidemics of foot–and–mouth disease

Streftaris

Gibson

2004

Proc. R. Soc. Lond. B

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We investigate the transmission dynamics of a certain type of foot-and-mouth disease (FMD) virus under experimental conditions. Previous analyses of experimental data from FMD outbreaks in non-homogeneously mixing populations of sheep have suggested a decline in viraemic level through serial passage of the virus, but these do not take into account possible variation in the length of the chain of viral transmission for each animal, which is implicit in the non-observed transmission process. We consider a susceptible-exposed-infectious-removed non-Markovian compartmental model for partially observed epidemic processes, and we employ powerful methodology (Markov chain Monte Carlo) for statistical inference, to address epidemiological issues under a Bayesian framework that accounts for all available information and associated uncertainty in a coherent approach. The analysis allows us to investigate the posterior distribution of the hidden transmission history of the epidemic, and thus to determine the effect of the length of the infection chain on the recorded viraemic levels, based on the posterior distribution of a p-value. Parameter estimates of the epidemiological characteristics of the disease are also obtained. The results reveal a possible decline in viraemia in one of the two experimental outbreaks. Our model also suggests that individual infectivity is related to the level of viraemia.

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“…Gibson and Renshaw, 1998;O'Neill andRoberts, 1999, Streftaris andGibson, 2004;Lekone andFinkenstädt, 2006, Cook et al, 2007), or Sequential Monte Carlo (SMC) routines (e.g. Doucet et al, 2001;Liu, 2001).…”

Section: Erratummentioning

confidence: 99%

Inference in Epidemic Models without Likelihoods

McKinley¹,

Cook²,

Deardon³

2009

The International Journal of Biostatistics

164

174

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Likelihood-based inference for epidemic models can be challenging, in part due to difficulties in evaluating the likelihood. The problem is particularly acute in models of large-scale outbreaks, and unobserved or partially observed data further complicates this process. Here we investigate the performance of Markov Chain Monte Carlo and Sequential Monte Carlo algorithms for parameter inference, where the routines are based on approximate likelihoods generated from model simulations. We compare our results to a gold-standard data-augmented MCMC for both complete and incomplete data. We illustrate our techniques using simulated epidemics as well as data from a recent outbreak of Ebola Haemorrhagic Fever in the Democratic Republic of Congo and discuss situations in which we think simulation-based inference may be preferable to likelihood-based inference. KEYWORDS:× exp − β N S t (i−1) I t (i−1) + δE t (i−1) + γI t (i−1) t (i) − t (i−1)

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Bayesian inference for stochastic epidemics in closed populations

Cited by 66 publications

References 11 publications

New model diagnostics for spatio-temporal systems in epidemiology and ecology

New model diagnostics for spatio-temporal systems in epidemiology and ecology

Bayesian analysis of experimental epidemics of foot–and–mouth disease

Inference in Epidemic Models without Likelihoods

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