Statistical genetics, statistical finance and other statistical problems

遗传学家定期收集关于人类数十万种遗传变异（例如基因表达）的数据，希望从中确定少数几种导致具有遗传成分的各种疾病，如糖尿病和癌症。然后使用统计方法来分析数据以完成任务。然而，这样的数据分析与经典统计方法旨在处理的数据分析大不相同。由于正在调查的候选人数量巨大，但样本数量有限，许多遗传变异可能纯粹是偶然的。发展统计学理论和方法来确定确定真正的遗传变异所需的证据的强度是一个深入研究的领域。本建议侧重于这一一般领域的问题。我们从模型选择的角度来看待统计问题。每一组遗传变异都可以用来建立一个预测疾病状态的统计模型。一个合理的标准是用来判断他们的相对优点，因此，使我们能够选择一个最佳的一个巨大的数量的候选人。这一发展有两个重要方面。首先，该标准必须适用于各种统计模型，并具有良好的理论特性。其次，该准则可以在没有非常高的计算复杂度的情况下实现。也就是说，计算策略应该与标准一起发展。我的研究沿着这些路线最近刚刚开始，并已取得了一些令人鼓舞的成功。

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.