Bayesian Nonparametric Inference for Stochastic Epidemic Models

了解传染性疾病的传播对于预防未来的重大暴发非常重要，因此它仍然是全球科学议程上的重要议题。人们普遍认识到，数学和统计模型已成为分析传染病动态的宝贵工具，它支持制定控制战略，为最高一级的决策提供信息，并在防治疾病传播方面发挥基本作用。尽管对有效参数估计方法的发展给予了极大的关注，但在非参数推理领域的活动相对较少。也就是说，在没有对其（参数）函数形式或属于某一参数分布族做出某些建模假设的情况下，对控制传播的数量进行推断，即i)感染力和ii)个体保持传染性的时间。拟议的研究涉及新方法的发展，该方法将能够在贝叶斯框架内对控制传播的参数进行非参数估计，并将拟议的方法应用于大型疾病暴发数据集。

Understanding the spread of communicable infectious diseases is of great importance in order to prevent major future outbreaks and therefore it remains high on the global scientific agenda. It has been widely recognised that mathematical and statistical modelling has become a valuable tool in the analysis of infectious disease dynamics by supporting the development of control strategies, informing policy-making at the highest levels, and in general playing a fundamental role in the fight against the spread of disease. Despite the enormous attention given to the development of methods for efficient parameter estimation, there has been relatively little activity in the area of non-parametric inference. That is, drawing inference for the quantities which govern transmission, i) the force of infection and ii) the period during which an individual remains infectious, without making certain modelling assumptions about its (parametric) functional form or that it belongs to a certain family of parametric distributions. The proposed research is concerned with the development of new methodology which will enable non-parametric estimation of the parameters which govern transmission within a Bayesian framework and the application of the proposed methods to large disease outbreak datasets.