Bayesian inference for epidemics with two levels of mixing

Demiris, Nikolaos; O’Neill, Philip D.

doi:10.1111/j.1467-9469.2005.00420.x

Cited by 33 publications

(32 citation statements)

References 16 publications

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“…Here R 0 = 2, m = 1 and the infectious period is exponential with mean 1. For clarity of scale, the probability of a final size of zero, 1/3, is not shown is briefly considered in Demiris and O'Neill (2005a;2005b), but the methods used are distinct from those we present here. Note that because final size data are non-temporal, it is not possible to infer temporal information such as the mean length of the infectious period.…”

Section: Bayesian Inferencementioning

confidence: 98%

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Computation of final outcome probabilities for the generalised stochastic epidemic

Demiris

O’Neill

2006

Stat Comput

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This paper is concerned with methods for the numerical calculation of the final outcome distribution for a well-known stochastic epidemic model in a closed population. The model is of the SIR (Susceptible→Infected→ Removed) type, and the infectious period can have any specified distribution. The final outcome distribution is specified by the solution of a triangular system of linear equations, but the form of the distribution leads to inherent numerical problems in the solution. Here we employ multiple precision arithmetic to surmount these problems. As applications of our methodology, we assess the accuracy of two approximations that are frequently used in practice, namely an approximation for the probability of an epidemic occurring, and a Gaussian approximation to the final number infected in the event of an outbreak. We also present an example of Bayesian inference for the epidemic threshold parameter.

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Section: Bayesian Inferencementioning

confidence: 98%

“…Gaussian approximations of the kind described below are often (explicitly or implicitly) used for the purposes of statistical inference, see for example Demiris and O'Neill (2005a) and the references therein. We first recall the relevant information (see Andersson and Britton, 2000, Section 4.4.)…”

Section: Gaussian Approximationmentioning

confidence: 99%

Computation of final outcome probabilities for the generalised stochastic epidemic

Demiris

O’Neill

2006

Stat Comput

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“…Ball, 1986;Becker, 1989;Rida, 1991and Demiris and O'Neill, 2005a,b, 2006. As a simple example consider the Abakaliki data with all of the temporal information removed, leaving the size of the initial susceptible population (N pop = 120) and the final epidemic size (N F = 30).…”

Section: Sir Model For Final Size Datamentioning

confidence: 99%

“…For comparison we use the SIR here, fitting to both removal time as well as final size data only (see e.g. Ball, 1986;Becker, 1989;Rida, 1991and Demiris and O'Neill, 2005a,b, 2006). An alternative, more detailed, version of this data set is available that allows more complex, and arguably more epidemiologically correct models to be fitted (see Eichner and Dietz, 2003).…”

Section: General Compartmental Epidemic Modelsmentioning

confidence: 99%

Simulation-based Bayesian inference for epidemic models

McKinley

Ross

Deardon

et al. 2014

Computational Statistics & Data Analysis

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A powerful and flexible method for fitting dynamic models to missing and censored data is to use the Bayesian paradigm via data-augmented Markov chain Monte Carlo (DA-MCMC). This samples from the joint posterior for the parameters and missing data, but requires high memory overheads for large-scale systems. In addition, designing efficient proposal distributions for the missing data is typically challenging. Pseudo-marginal methods instead integrate across the missing data using a Monte Carlo estimate for the likelihood, generated from multiple independent simulations from the model. These techniques can avoid the high memory requirements of DA-MCMC, and under certain conditions produce the exact marginal posterior distribution for parameters. A novel method is presented for implementing importance sampling for dynamic epidemic models, by conditioning the simulations on sets of validity criteria (based * Corresponding author. Tel.: (+44) 1223 337685.Email address: tjm44@cam.ac.uk (Trevelyan J. McKinley) January 16, 2013 on the model structure) as well as the observed data. The flexibility of these techniques is illustrated using both removal time and final size data from an outbreak of smallpox. It is shown that these approaches can circumvent the need for reversible-jump MCMC, and can allow inference in situations where DA-MCMC is impossible due to computationally infeasible likelihoods. Preprint submitted to Elsevier

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“…Rida, 1991;Demiris and O'Neill, 2005b). Since prophylactic measures aim to achieve R * ≤ 1, assuming that R * > 1 is not desirable while it also results in underestimating the variability of the model parameters.…”

Section: Threshold Parametermentioning

confidence: 99%

On the Epidemic of Financial Crises

2012

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This paper proposes a framework for modelling financial contagion that is based on SIR (Susceptible-Infected-Recovered) transmission models from epidemic theory. This class of models addresses two important features of contagion modelling, which are a common shortcoming of most existing empirical approaches, namely the direct modelling of the inherent dependencies involved in the transmission mechanism, and an associated canonical measure of crisis severity. The proposed methodology naturally implies a control mechanism, which is required when evaluating prospective immunisation policies that intend to mitigate the impact of a crisis. It can be implemented not only as a way of learning from past experiences, but also at the onset of a contagious financial crisis. The approach is illustrated on a number of currency crisis episodes, using both historical final outcome and temporal data. The latter require the introduction of a novel hierarchical model that we call the Hidden Epidemic Model (HEM), and which embeds the stochastic financial epidemic as a latent process. The empirical results suggest, among other, an increasing trend for global transmission of currency crises over time.

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Bayesian inference for epidemics with two levels of mixing

Cited by 33 publications

References 16 publications

Computation of final outcome probabilities for the generalised stochastic epidemic

Computation of final outcome probabilities for the generalised stochastic epidemic

Simulation-based Bayesian inference for epidemic models

On the Epidemic of Financial Crises

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