Bayesian Non-Parametric Methodology for Stochastic Epidemic Models

对随机流行病模型进行模拟和推理是了解和控制传染病传播的关键策略。尽管参数估计的方法受到了极大的关注，但在非参数推断领域的活动相对较少。也就是说，在不对其函数形式做出具体的建模假设的情况下，对感染率进行推断。在这个项目中，我们考虑了异质性混合模型，其中两个个体之间的感染率是其特征的函数，例如位置或类型。我们开发了一种新的非参数推导函数的方法，消除了做出有问题的参数假设的需要。我们采用贝叶斯方法，通过赋予感染率函数一个高斯过程的先验分布，然后发展了一种有效的数据增广马尔可夫链蒙特卡罗方法来估计感染率函数、GP超参数和未观察到的感染时间。我们将使用模拟数据和来自荷兰的禽流感暴发数据来说明我们的方法。

Simulating from and making inference for stochastic epidemic models are key strategies for understanding and controlling the spread of infectious diseases. Despite the enormous attention given to methods for parameter estimation, there has been relatively little activity in the area of nonparametric inference. That is, drawing inference for the infection rate without making specific modelling assumptions about its functional form. In this project we are concerned with heterogeneously mixing models in which the infection rate between two individuals is a function of their characteristics, for example location or type. We develop a novel method for inferring the function nonparametrically, removing the need to make questionable parametric assumptions. We adopt a Bayesian approach by assigning a Gaussian Process prior distribution to the infection rate function and then develop an efficient data augmentation Markov Chain Monte Carlo methodology to estimate the infection rate function, the GP hyperparameters and the unobserved infection times. We will illustrate our methodology using simulated data and as well as data on an Avian Influenza outbreak from the Netherlands.