Advancing statistical inference for correlated and partially observed data

真实世界的数据非常复杂，很少满足“教科书”方法的假设。例如，进化和流行病学研究违反了观察之间相互独立的传统假设，因为现在的观察总是取决于过去发生的事情。因此，现有的理论和方法不能分析这些类型的数据，需要新的发展。此外，科学家通常不可能连续地观察一切，因此数据往往是部分观察的。此外，不可观测事件的空间可能如此巨大，以至于标准的计算方法失败，或者充其量有非常长的计算时间。这项研究计划旨在开发新的理论和方法来解决这些紧迫的问题。具体地说，该研究计划将重点放在用于分析来自进化生物学和流行病学的相关和部分观察数据的推断方法。*统计方法在进化研究中发挥着非常重要的作用，因为它们为回答宏观进化中的许多重要问题提供了严格的工具，例如所有物种是否都是共同祖先的后代，人类是如何迁出非洲的，以及艾滋病毒-1是如何在非洲中部传播的。同样，统计推断通过衡量持续暴发的严重性和预测未来的风险，为控制传染病流行提供了必要的信息。因此，正确和有效地进行这些分析是至关重要的，遗憾的是，目前的方法并非如此。该研究计划将通过建立所需的理论、开发新的方法和实施有效的软件来处理进化和流行病学数据来解决这一问题。*这项提议的影响将从三个方向延伸。首先，科学发现将直接影响进化和流行病学研究。其次，这项工作的结果还将影响其他研究领域，因为相关和部分观察到的数据不仅限于进化生物学和流行病学。最后，该研究计划将招募和培训下一代聪明的数学和统计头脑，以应对现代数据带来的挑战。

Real-world data are very complicated and rarely satisfy the assumptions of "textbook" approaches. For example, a traditional assumption of independence between observations is violated for evolutionary and epidemiological studies because observations from the present always depend on what happened in the past. Therefore, existing theory and methods are not capable of analyzing these types of data, necessitating new developments. Additionally, it is usually not feasible for scientists to observe everything continuously, thus data are often partially observed. In addition, the space of unobservable events can be so massive that standard computational methods fail or, at best, have very long computation times. This research program aims to develop novel theory and methods for tackling these pressing problems. Specifically, the research program will focus on inference methods for analyzing correlated and partially observed data from evolutionary biology and epidemiology.******Statistical methods play a very important role in evolutionary studies because they provide rigorous tools for answering many important questions in macroevolution such as whether all species are descended from a common ancestor, how humans migrated out of Africa, and how HIV-1 spread in central Africa. Similarly, statistical inference provides essential information for controlling infectious disease epidemics by measuring the severeness of an ongoing outbreak and predicting future risks. Therefore, it is vital that these analyses are done correctly and efficiently, which is unfortunately not the case for current approaches. The research program will fix this problem by establishing the needed theory, developing new methods and implementing efficient software for handling evolutionary and epidemiological data.******The impacts of this proposal will extend in three directions. Firstly, the scientific findings will directly impact evolutionary and epidemiological studies. Secondly, the results of this work will also impact other research areas because correlated and partially observed data are not only restricted to evolutionary biology and epidemiology. Finally, the research program will recruit and train the next generation of bright mathematical and statistical minds to address challenges arising from modern data.