Stochastic Modelling

随机区室模型和性状进化模型是研究传染病流行动力学的有力工具。然而，缺乏严谨的理论和有效的计算方法阻碍了这些模型对实际数据的适用性。拟议中的研究计划旨在直接切入这一紧迫挑战的核心。我有三个具体目标。第一个目标是建立随机区室模型来研究流行病的动力学。较高的计算成本阻碍了这些模型的适用性。最近，我开发了计算随机区室模型转移概率的快速算法。在这些算法的基础上，我将为随机区隔模型设计一个有效的直接推理框架。这一框架将包括许多实际功能，例如检测流行病动态的变化以及纳入新信息的能力。我的新进展将为研究流行病的传播提供更好的工具，从而将对防治新出现的传染病流行病作出重大贡献。第二个目标是建立性状进化模型的理论，以探索病原体的起源和传播。尽管被广泛用于研究传染病流行的动力学，但许多性状进化模型的统计特性仍然未知。默认这些模型的标准统计理论会导致资源浪费在非信息性样本和错误的分析解释上。提出的研究计划将通过为性状进化模型建立严格的理论来解决这个问题。最终目标是通过机器学习开发基于模拟的方法，为流行病学和进化数据建立有效的推理方法。在实践中，我们可能需要使用过于复杂而无法应用直接推理的模型。该方向的结果为这些模型提供了一种有效的推理方法。

Stochastic compartmental models and trait evolution models are powerful tools for studying the dynamics of infectious disease epidemics. However, the lack of rigorous theory and efficient computational methods has hindered the applicability of these models to real-world data. The proposed research program aims to cut directly to the heart of this pressing challenge. I have three specific objectives.The first objective is fostering stochastic compartmental models to study the dynamics of epidemics. The high computational cost has hindered the applicability of these models. Recently, I have developed fast algorithms for computing the transition probabilities of stochastic compartmental models. Building upon these algorithms, I will design an efficient direct inference framework for stochastic compartmental models. This framework will include many practical features, such as detecting changes in the dynamics of epidemics and the ability to incorporate new information. My new developments will provide better tools for studying the spread of epidemics, thus will contribute significantly to the battle against emerging infectious disease epidemics.The second objective is establishing theory for trait evolution models to explore the origin and spread of pathogens. Despite being used widely for studying the dynamics of infectious disease epidemics, the statistical properties of many trait evolution models remain unknown. Tacitly assuming the standard statistical theory for these models can lead to wasting resources on non-informative samples and incorrect interpretation of the analysis. The proposed research program will address this problem by building rigorous theory for trait evolution models.The final objective is developing a simulation-based method via machine learning to build efficient inference methods for epidemiological and evolutionary data. In practice, we may need to use models that are too complex to apply direct inference. The outcome of this direction is providing an efficient inference method for these models.