Statistical genetics, statistical finance and other statistical problems

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Data on hundreds of thousands of genetic variations (e.g. gene expressions) of human beings are routinely collected by geneticists in the hope of identifying, among them, a handful that are responsible for various diseases having a genetic component, such as diabetes and cancers. Statistical methods are then used to analyze the data to complete the task. Yet such data analyses are far different from the ones that classical statistical methods are designed to deal with. With huge number of candidates under investigation but limited number of samples, many genetic variations can appear to be culprits purely by chance. Developing statistical theories and methods to determine the strength of evidence needed to identify the true set of responsible genetic variations is an area of intensive research. This proposal focuses on problems in this general area. We view the statistical problem from a model selection angle. Every group of genetic variations can be used to construct a statistical model to predict the disease status. A sensible criterion is used to judge their relative merits, and therefore, enables us to select an optimal one among a huge number of candidates. There are two important aspects in this development. First, the criterion must be adaptable to various statistical models with well understood good theoretical properties. Secondly, the criterion can be implemented without an exceedingly high computational complexity. That is, computational strategy should be developed together with the criterion. My research along these lines has just been started recently and has already met with some encouraging successes.