Sequential, nonsequential, and shrinkage inference techniques and applications

针对临床试验、毒理学计数数据、复杂疾病的遗传连锁分析、工业质量控制和微阵列数据分析等领域中的各种统计分析问题，本研究提出了几种改进的方法，特别是在感兴趣的参数空间受限的情况下，提出了检验统计假设的序贯方法。一般来说，如果我们知道参数受到一些约束的限制，那么我们有理由预计，包含这些限制的测试程序应该比那些忽略它们的测试程序更强大。发生这种情况的一个模型的例子是，当测试某个给定基因是否与某些疾病有关时，在不同基因座上存在可能也导致疾病的其他基因时，就会出现这种情况。在这种情况下，重组体的数量(衡量连锁程度的一种指标)为二项混合。为这类基因研究收集数据需要多年和大量的财政支持。我提出的方法将包括这种类型的假设检验，预计将减少决策所需的总样本。此外，本项目中提出的收缩序贯估计方法有望减少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，因为基因芯片的成本相当高。我建议的其他方法是用于分析计数数据的经验贝叶斯方法。预计这些方法也能更有效地估计平均计数，同时纳入以辅助信息(协变量或预测因素)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).