Bayesian statistics and computation: applications in finance and biology

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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.