New Methodology for Multiple Testing and Simultaneous Inference

研究者为多重测试和同时推理问题开发了新的方法和理论。处理多重性的一种经典方法是要求决策规则控制家族错误率。但是，当测试的数量很大时，这种测量是如此严格，以至于其他假设几乎没有机会被发现。因此，在有限样本和渐近情况下研究了误差控制的备选措施。这些措施包括：虚假发现率；k次或更多次错误拒绝的概率；错误发现比例的尾部概率。为了开发不依赖于不现实或无法验证的模型假设的方法，研究者广泛使用计算机密集型方法。重采样的力量在于可以捕获单个测试的联合依赖结构，因此方法不必过于保守。从理论、计算和理论的角度对这种方法的追求进行了调查，特别强调了大量的测试。本研究的目的是为多重推理问题提供新的理论和方法。实际上，任何科学实验都是为了回答有关被调查过程的问题，这些问题通常可以正式转化为一组有待检验的假设。只有一个例外，即只研究一个假设或问题。在“信息时代”，统计学家面临的挑战是解释复杂数据分析所导致的所有可能的错误，以便任何有趣的结论都可以可靠地视为真实的结构，而不是“数据窥探”的结果，即发现随机数据的人工制品。例如，目前的生物技术和基因组学方法产生了DNA微阵列实验，在这些实验中，细胞中数千个基因的基因表达水平被同时逐个基因地分析。因此，我们的目标是设计出新的技术，这些技术不是基于在面对大量数据时有效处理多样性问题的强大假设。由此产生的推理工具可以应用于遗传学、计量经济学、金融、脑成像、临床试验、教育和天文学等不同领域。

The investigator develops new methods and theory for problems in multiple testing and simultaneous inference. A classical approach to dealing with multiplicity is to require that decision rules control the familywise error rate. But, when the number of tests is large, this measure is so stringent that alternative hypotheses have little chance of being detected. Thus, alternative measures of error control are studied both in finite sample and asymptotically. Such measures include: the false discovery rate; the probability of k or more false rejections; tail probabilities of the false discovery proportion. In order to develop methods which do not rely on unrealistic or unverifiable model assumptions, the investigator makes extensive use of computer-intensive methods. The power of resampling is that the joint dependence structure of the individual tests can be captured so that methods need not be overly conservative. The pursuit of such methodology is investigated from theoretical, computational and theoretical points of view, with special emphasis on a large number of tests.The goal of this research is to develop new theory and methods for problems of multiple inference. Virtually any scientific experiment sets out to answer questions about the process under investigation, which often can be translated formally into a set of hypotheses to be tested. It is the exception that only a single hypothesis or question is under study. In the "information age", the statistician is faced with the challenge of accounting for all possible errors resulting from a complex data analysis, so that any interesting conclusions can reliably be viewed as real structure rather than the result of "data snooping", i.e. finding artifacts of random data. For example, current methods in biotechnology and genomics generate DNA microarray experiments, where gene expression level in cells for thousands of genes are analyzed simultaneously on a gene by gene basis. The goal then is to devise new techniques that are not based on strong assumptions that effectively deal with problems of multiplicity in the face of vast amounts of data. The resulting inferential tools can be applied to such diverse fields as genetics, econometrics, finance, brain imaging, clinical trials, education and astronomy.