Bayesian nonparametric inference for stochastic epidemic models

• Main Author: Xu, Xiaoguang
• Published: University of Nottingham 2015
• Subjects: 519.5; QA276 Mathematical statistics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.674839

Modelling of infectious diseases is a topic of great importance. Despite the enormous attention given to the development of methods for efficient parameter estimation, there has been relatively little activity in the area of nonparametric inference for epidemics. In this thesis, we develop new methodology which enables nonparametric estimation of the parameters which govern transmission within a Bayesian framework. Many standard modelling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. We relax these assumptions and analyse data from disease outbreaks in a Bayesian nonparametric framework. We first apply our Bayesian nonparametric methods to small-scale epidemics. In a standard SIR model, the overall force of infection is assumed to have a parametric form. We relax this assumption and treat it as a function which only depends on time. Then we place a Gaussian process prior on it and infer it using data-augmented Markov Chain Monte Carlo (MCMC) algorithms. Our methods are illustrated by applications to simulated data as well as Smallpox data. We also investigate the infection rate in the SIR model using our methods. More precisely, we assume the infection rate is time-varying and place a Gaussian process prior on it. Results are obtained using data augmentation methods and standard MCMC algorithms. We illustrate our methods using simulated data and respiratory disease data. We find our methods work fairly well for the stochastic SIR model. We also investigate large-scaled epidemics in a Bayesian nonparametric framework. For large epidemics in large populations, we usually observe surveillance data which typically provide number of new infection cases occurring during observation periods. We infer the infection rate for each observation period by placing Gaussian process priors on them. Our methods are illustrated by the real data, i.e. a time series of incidence of measles in London (1948-1957). Please note, the pagination in the online version differs slightly from the official, printed version because of the insertion of a list of corrections. The incorporation of the corrections into the text of the online version means that the page breaks appear at different points on p. 39-47, and p. 47-147 of the electronic version correspond to p. 48-148 of the printed version.