Sequential, nonsequential, and shrinkage inference techniques and applications

本研究提出了几种改进的方法，以处理相关领域的各种统计分析问题，如临床试验，在毒理学中产生的计数数据，复杂疾病的遗传连锁分析，工业质量控制，和微阵列数据analysis.Specifically，我提出了序贯的方法来检验统计假设时，参数空间的利益受到限制。一般来说，如果我们知道参数受到某些约束的限制，那么我们就有理由期望，包含这些约束的测试程序应该比忽略它们的测试程序更强大。 这种情况发生的模型的一个例子是，在不同基因座上的其他基因也可能导致某种疾病的情况下，测试给定基因是否导致某种疾病时产生的模型。在这种情况下，重组体的数量（连锁程度的量度） 都是二项混合为这种遗传研究收集数据需要多年时间和大量的财政支持。我建议的方法将包括这种类型的假设检验，并有望减少决策所需的总样本。此外，收缩序贯估计方法在这个项目中提出的，预计将减少DNA微阵列数据分析所需的样本量，同时借用跨基因的信息。这一点很重要，因为微阵列的成本相当高。我建议的其他方法是用于计数数据分析的经验贝叶斯方法。预计这些方法在估计平均计数方面也更有效，同时结合了以辅助信息（协变量或预后因素）形式提供的先验知识。

This research proposes several improved methologies to deal with various statistical analysis problems of relevance in areas such as clinical trials, count data arising in toxicology, genetic linkage analysis of complex diseases, industrial quality control, and microarray data analysis.Specifically, I am proposing sequential methods for testing statistical hypotheses when the parameter space of interest is constrained. In general, if we know that parameters are restricted by some constraints then it is reasonable to expect that testing procedures incorporating the restrictions should be more powerful than those ignoring them.  An example of a model in which this happens is the one arising when testing whether or not a given gene is responsible for certain disease in the presence of other genes at different loci that may also be responsible for the disease. In such cases, the number of recombinants (a measure of the degree of linkage)   has a binomial mixture. Collecting data for such genetic studies requires many years and large financial support. The methods I am proposing will include hypotheses testing of this type and are expected to reduce the total sample needed for making decision. Moreover, the shrinkage sequential estimation methods proposed in this project are expected to reduce the sample size needed in DNA microarray data analysis while borrowing information across the genes. This is important, as the cost of a  microarray is quite high.Other methods in my proposal are empirical Bayes methods for the analysis of count data. These methods are also expected to be more efficient in estimating the average count and at the same time incorporating prior knowledge that is available in the form of auxiliary information (covariates or prognostic factors).