Advancing statistical inference for correlated and partially observed data

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.