Bayesian statistics and computation: applications in finance and biology

科学程序的改进使研究人员有能力细致地观察现实世界。例如，在生物学中，新技术使科学家能够尽可能详细地测量生物体的结构、活动和功能。在其他快速数据收集领域，如医疗监测、信号处理和金融行业，通常会收集大量数据。从现有数据中提取尽可能多的有用信息是一项持续的挑战。这主要是对统计学家的挑战，并激励我在研究计划中详细介绍的工作。我建议研究使用现代先进的统计方法来分析来自生物系统的观测数据（广义上称为生物信息学或计算生物学），以及数据随时间顺序观察的应用（称为时间序列分析），特别是在与金融相关的应用中。在生物学中，挑战的范围从细胞图像的分析，基因水平上的遗传活动的测量，在分子水平上的基因结构的分析，直到整个生物系统的分析。在时间序列中，挑战包括分析高频数据（例如，逐秒记录的数据）和分析多个数据序列的联合变化。我的工作将帮助和告知在这些领域工作的科学家和研究人员。此外，我的目标是使受过数学训练的研究人员具备与应用专家合作的技能。

Improvements in scientific procedures have granted researchers the ability to observe the real world in minute detail.  For example, in biology, new technology has allowed scientists to measure the structure, activity and function of organisms in the finest possible detail. In other, rapid data gathering areas, such in medical monitoring, signal processing, and the financial industry, vast amounts of data are routinely gathered.  There is an ongoing challenge to extract the greatest possible amount of useful information from the data available.  This is primarily a challenge to statisticians, and motivates the work detailed in my research proposal.I propose to research in the use of modern advanced statistical methods in the analysis of observed data derived from biological systems (broadly termed bioinformatics or computational biology) and also from applications where data are observed sequentially through time (termed time series analysis), particularly in applications relevant to the finance.In biology, challenges range from the analysis of cell images, measurements of genetic activity at the gene level, the analysis of gene structure at the molecular level up to the analysis of whole biological systems.  In time series, challenges include the analysis of high-frequency data (say, data recorded second-by-second) and the analysis of joint variation of multiple data series.My work will assist and inform scientists and researchers working in each of these fields. Furthermore, I aim to equip mathematically trained researchers with the skills to work with application specialists.