Stochastic Modelling

随机建模

• 批准号: CRC-2021-00239
• 负责人: Ho, Lam
• 金额: $ 5.46万
• 依托单位: Dalhousie University
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=750788
• 关键词: Stochastic; Modelling

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.

随机房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，缺乏严格的理论和有效的计算方法，阻碍了这些模型的适用性，以现实世界的数据。拟议的研究计划旨在直接切入这一紧迫挑战的核心。我有三个具体的目标，第一个目标是建立随机的房室模型来研究流行病的动力学。高计算成本阻碍了这些模型的适用性。最近，我开发了快速算法计算随机房室模型的转移概率。基于这些算法，我将设计一个有效的随机房室模型的直接推理框架。这一框架将包括许多实用的特点，如检测流行病动态的变化和纳入新信息的能力。我的新进展将为研究流行病的传播提供更好的工具，从而将对与新兴传染病流行病的斗争做出重大贡献。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，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可能会导致在非信息样本上浪费资源和对分析的错误解释。该研究计划将通过建立严格的性状进化模型理论来解决这一问题，最终目标是通过机器学习开发一种基于模拟的方法，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的模型来应用直接推理。这一方向的成果是为这些模型提供了一种有效的推理方法。