Statistical genetics, statistical finance and other statistical problems

遗传学家定期收集有关人类数十万种遗传变异（例如基因表达）的数据，希望从中找出少数几种与具有遗传成分的各种疾病（如糖尿病和癌症）有关的变异。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所要处理的数据有很大的不同。由于正在调查的候选者数量庞大，但样本数量有限，许多遗传变异可能纯粹是偶然的。发展统计理论和方法，以确定确定真正负责任的遗传变异所需证据的强度，是一个深入研究的领域。这一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。每组遗传变异都可以用来构建一个预测疾病状态的统计模型。一个合理的标准被用来判断它们的相对优点，从而使我们能够在大量的候选中选择一个最优的。这一发展有两个重要方面。首先，该准则必须适用于具有良好理论性质的各种统计模型。其次，该准则的实现不需要太高的计算复杂度。也就是说，计算策略应该与准则一起发展。我在这方面的研究最近才刚刚开始，并且已经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.