Inference under Selection and Model Uncertainty

这个项目有两个不同的部分，每个部分都由基因组实验中的推理问题提出。 第一个问题的出现是因为，通常情况下，数千个基因被筛选，而选择更少的基因进行进一步研究。 统计推断必须考虑这种选择机制，否则实际置信系数小于标称水平，并且随着基因数量的增加而接近零。我们的目标是构建有效的频率置信区间的平均值选定的人口。这将为错误发现率提供替代置信区间。 第二个问题涉及模型不确定性下的推理，其目标是考虑模型集合引起的可变性。 在这里，贝叶斯的方法，寻求构建区间占模型的不确定性，调查的先验模型空间的选择的影响，并构建新的搜索算法，利用并行处理的优势，可用于情况下，当有更多的协变量比observations.The工作将在基因组研究和高性能计算的影响。 首先，对于基因组研究的推断，将提供有效的统计程序来筛选结果。确保推论是有效的是至关重要的，正如最近《纽约时报》的一篇文章所说明的那样，由于错误的统计推断，基因组疾病治疗被发现是无用的（“癌症测试中的光明前景如何崩溃”，《纽约时报》，2011年7月7日）。 其次，将开发使用高性能计算的并行处理算法。这些算法利用了通常可用的大量处理器，并将大型基因组选择问题拆分到许多处理器上。 这导致来自这些统计程序的答案可以在真实的时间内可用，并且因此在临床环境中是相关的。

This project has two distinct parts, each suggested by problems of inference in genomic experiments. The first problem arises because, typically, thousands of genes are screened, and a smaller number are selected for further study. Statistical inference must take this selection mechanism into account, otherwise the actual confidence coefficient is smaller than the nominal level, and approaches zero as the number of genes increases. The goal is to construct valid frequentist confidence intervals for the means of the selected populations. This will provide a confidence interval alternative to the False Discovery Rate. The second problem deals with inference under model uncertainty, where the goal is to account for the variability induced by the collection of models. Here a Bayesian approach is taken, seeking to construct intervals accounting for model uncertainty, investigate the impact of the choice of priors on model space, and construct new search algorithms that take advantage of parallel processing and can be used in the case when there are more covariates than observations.The work will have impact in both genomic studies and high performance computing. First, for inference from genomic studies, a valid statistical procedure to screen results will be provided. Insuring that the inferences are valid is of crucial importance, as illustrated by a recent NY Times article where a genomic disease therapy was found to be useless, because of faulty statistical inference (``How Bright Promise in Cancer Testing Fell Apart", NY Times, July 7, 2011). Second, parallel processing algorithms, using high performance computing, will be developed. These algorithms take advantage of the abundance of processors typically available, and split the large genomic selection problem across the many processors. This results in answers from these statistical procedures that can be available in real time, and thus be relevant in a clinical setting.