Bayesian model assessment for stochastic epidemic models

Acrucial practical advantage of infectious diseases modelling as a public health tool lies in its application to evaluate various disease-control policies. However, such evaluation is of limited use, unless a sufficiently accurate epidemic model is applied. If the model provides an adequate fit, it is possible to interpret parameter estimates, compare disease epidemics and implement control procedures. Methods to assess and compare stochastic epidemic models in a Bayesian framework are not well-established, particularly in epidemic settings with missing data. In this thesis, we develop novel methods for both model adequacy and model choice for stochastic epidemic models. We work with continuous time epidemic models and assume that only case detection times of infected individuals are available, corresponding to removal times. Throughout, we illustrate our methods using both simulated outbreak data and real disease data. Data augmented Markov Chain Monte Carlo (MCMC) algorithms are employed to make inference for unobserved infection times and model parameters. Under a Bayesian framework, we first conduct a systematic investigation of three different but natural methods of model adequacy for SIR (Susceptible-Infective-Removed) epidemic models. We proceed to develop a new two-stage method for assessing the adequacy of epidemic models. In this two stage method, two predictive distributions are examined, namely the predictive distribution of the final size of the epidemic and the predictive distribution of the removal times. The idea is based onlooking explicitly at the discrepancy between the observed and predicted removal times using the posterior predictive model checking approach in which the notion of Bayesian residuals and the and the posterior predictive p−value are utilized. This approach differs, most importantly, from classical likelihood-based approaches by taking into account uncertainty in both model stochasticity and model parameters. The two-stage method explores how SIR models with different infection mechanisms, infectious periods and population structures can be assessed and distinguished given only a set of removal times. In the last part of this thesis, we consider Bayesian model choice methods for epidemic models. We derive explicit forms for Bayes factors in two different epidemic settings, given complete epidemic data. Additionally, in the setting where the available data are partially observed, we extend the existing power posterior method for estimating Bayes factors to models incorporating missing data and successfully apply our missing-data extension of the power posterior method to various epidemic settings. We further consider the performance of the deviance information criterion (DIC) method to select between epidemic models