Theory and Methods for Multiple Testing and Inference

多重测试和推理的理论和方法

• 批准号: 0404979
• 负责人: Joseph Romano
• 金额: $ 9万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0404979&HistoricalAwards=false
• 关键词: Theory; Methods; Multiple; Testing; Inference

Principal Investigator: Joseph P RomanoProposal Title: Theory and methods for Multiple Testing Proposal Id: DMS - 0404979AbstractThe main goal of this research proposal is the development of theory and methodology for problems in multiple testing and inference. A classical approach to dealing with multiplicity is to require decision rules that control the familywise error rate (FWER), the probability of rejecting at least one true hypothesis. But when the number of tests is large, control of the FWER is so stringent that alternative hypotheses have little chance of being detected. In response, the false discovery rate (FDR) of Benjamini and Hochberg has gained wide use.Alternative measures, such as the probability of rejecting k or more true hypotheses, or ones based directly of the actual false discovery proportion (FDP) will be considered by the investigator. For each measure of error control, it is desired to construct procedures that exhibit error control under the weakest possible assumptions. Subject to error control, the procedures should be efficient in their ability to detect alternative hypotheses. The main approach used to develop methods that do not rely on unrealistic or unverifiable model assumptions will be the use of the bootstrap, subsampling, and other computer-intensive methods. These tools offer viable approaches to obtaining valid distributional approximations while assuming very little about the stochastic mechanism generating the data. Just as resampling has been enormously successful in the case of questions of a single inference, its use can be extended fruitfully to questions of multiple inferences.While such an approach has been used with some success, its full potential is currently unrealized and it is clear that efficient and more broadly applicable methods will be advanced in the next few years. The power of the bootstrap and related methods is that the joint dependency structure of the individual test statistics can be captured so that methods need not be overly conservative. The pursuit of such new methodology will be investigated from theoretical, computational and practical points of view. Notably, the investigator will address the multiple inference problem when the number of hypotheses is large compared with sample size, the open problem of directional errors, as well as the construction of efficient techniques that control the FDR, as well as other measures of error.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. It is the exception that a single hypothesis is considered. Moreover, due to effects of "data snooping" (or "data mining"), other inference questions arise as well.The statistician is then faced with the challenge of accounting for all possible errors resulting from a complex data analysis, so that any resulting inferences or interesting conclusions can reliably be viewed as real structure rather than artifacts of random data. While the history of statistical methods that deal with problems of simultaneous inference data back at least half a century, most of the classical techniques typically rely on strong assumptions, or they are inefficient. Driven by the advent of computers and the information age, there has been a growing demand for more reliable and efficient methods for multiple testing. For example, current methods in biotechnology and genomics generate DNA microarray experiments, where expression levels in cells for thousands of genes must be analyzed simultaneously. Similar problems arise in image processing, such as neuroimaging, and econometrics. It is now not uncommon to encounter data consisting of megabytes of information. Thus, the statistician is faced with new challenges of devising techniques that are not based on strong assumptions and can effectively deal with problems of multiplicity in the presence of vast amounts of data.

主要研究者：Joseph P Romano提案标题：理论和方法的多重测试建议Id：DMS -0404979摘要本研究建议的主要目标是发展的理论和方法的问题，在多重测试和推理。 处理多重性的一个经典方法是要求控制族错误率（FWER）的决策规则，即拒绝至少一个真实假设的概率。 但是，当测试的数量是大的，控制的FWER是如此严格，替代假设几乎没有机会被检测到。 作为回应，Benjamini和Hochberg的错误发现率（FDR）得到了广泛的使用。替代措施，如拒绝k个或更多真实假设的概率，或直接基于实际错误发现比例（FDP）的措施将被研究者考虑。 对于误差控制的每一个测量，都希望构造在最弱的可能假设下表现出误差控制的过程。 在误差控制的前提下，这些程序应当能够有效地发现备选假设。 用于开发不依赖于不现实或无法验证的模型假设的方法的主要方法将是使用自举、二次抽样和其他计算机密集型方法。 这些工具提供了可行的方法来获得有效的分布近似值，而很少假设产生数据的随机机制。 就像rescue在单一推理的问题中取得了巨大的成功一样，它的使用也可以是 虽然这种方法已经取得了一些成功，但其全部潜力目前尚未实现，很明显，在未来几年内将提出有效和更广泛适用的方法。 Bootstrap和相关方法的强大之处在于，可以捕获单个检验统计量的联合依赖结构，因此方法不需要过于保守。 将从理论、计算和实践的角度来研究这种新方法的追求。 值得注意的是，研究者将解决多重推理问题时，假设的数量是大样本量，方向错误的开放性问题，以及建设有效的技术，控制FDR，以及其他措施的错误。几乎任何科学实验着手回答有关的过程中调查的问题，这通常可以正式地转化为一系列假设。 唯一的例外是只考虑一个假设。 此外，由于“数据窥探”（或“数据挖掘”）的影响，其他推理问题也随之出现，统计学家面临着一个挑战，即考虑到复杂数据分析中可能出现的所有错误，以便任何由此产生的推理或有趣的结论都可以可靠地被视为真实的结构，而不是随机数据的伪影。虽然处理同时推理数据问题的统计方法的历史至少可以追溯到半个世纪，但大多数经典技术通常依赖于强假设，或者效率低下。 随着计算机和信息时代的到来，人们越来越需要更可靠、更有效的多重测试方法。 例如，目前的生物技术和基因组学方法产生DNA微阵列实验，其中必须同时分析细胞中数千个基因的表达水平。类似的问题出现在图像处理中，如神经成像和计量经济学。 现在遇到由兆字节信息组成的数据并不罕见。 因此，统计人员面临着新的挑战，即设计出不以强有力的假设为基础的技术，并能有效地处理大量数据中的多重性问题。