Statistical Theory and Methodology

统计理论与方法

• 批准号: 0505673
• 负责人: Bradley Efron
• 金额: $ 31万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505673&HistoricalAwards=false
• 关键词: Statistical; Theory; Methodology

ABSTRACTProp ID: DMS-050 5673 PI: Efron, Bradley and Diaconis, PersiNSF Program: STATISTICS Institution: Stanford University Title: Statistical Theory and Methodology LARGE-SCALE SIMULTANEOUS TESTING (Bradley Efron) This investigator is studying the analysis of large-scale simultaneous hypothesistesting situations, for example a microarray experiment searching for genes thatbehave differently in HIV positive or negative subjects. A simplemethodology is being developed that requires a minimum of frequentist orBayesian modelling assumptions, and provides for both the efficientselection of the non-null cases, and the estimation of effect sizes. In classical terminology, both size and power are assessed.This methodology depends on false discovery rate calculations, implemented via empirical Bayes techniques. A typical result might report"there are 200 of the 10,000 genes that can be clearly identified asdifferentially expressed between the two groups of subjects, but there arealso about 800 other non-null genes that this experiment was not powerfulenough to detect."Classical 20th Century statistical theory was fashioned to handle smallproblems, dozens or maybe hundreds of data points, with one or maybe a fewunknown parameters. 21st Century scientific technology now provides massivedata sets, with millions of individual measurements and thousands ofparameters to consider all at once. Microarrays are the prime example, butsimilar problems arise from a variety of devices: proteomic chips, time offlight spectroscopy, flow cytometry, and fMRI scanners. The goal of thisresearch is an efficient, computationally efficient methodology for analyzingmassive simultaneous testing problems, without the need for extensivemodelling assumptions.MONTE CARLO METHODS IN PROBABILITY AND STATISTICS (Persi Diaconis)The main focus of this investigation is on rates of convergence of Monte Carloand Markov chain algorithms for statistical computation. One aspect is phase transitions ( cut-off phenomena), extending Diaconis' recent solution ofthe Peres conjecture (joint with Saloff-Coste). The workincludes creating new algorithms using computational tools such as Grobnerbases and combinatorial characterizations such as Tuttes f-factors. This alsocontributes to Bayesian methodology studying prior distributions for Markovchains, non-parametrics andcomputational tools. A final focus is the development of group theoreticcharacter theories in non-standard situations such asunipotent groups and Hecke algebras.Probability models underlie many areas of modern scientific study, but theyraise puzzling and important questions concerning the connection of themodel with real world phenomena. Diaconis studiesfoundational topics such as `what does it mean to say coin flips arerandom'? This recently led to the discovery (joint with Susan Holmes andRichard Montgomery) that in fact, natural human coin flips show a small butsignificant bias (about 51% come up the same as the previous flip).Careful looks at the assumptions, justification andvalidity of `randomness' apply to widely-used simulation methods (how longshould an algorithm be run until its job is done?). Weather forcastingand air pollution are just two of the areas that require the dependabilityof such simulations.

摘要项目ID：DMS-050 5673 PI：Efron、布拉德利和Diaconis，PersiNSF项目：统计 机构：斯坦福大学标题：统计理论与方法 大规模同步测试（布拉德利埃夫隆）这位研究者正在研究大规模同步假设测试情况的分析，例如，一个微阵列实验，寻找在HIV阳性或阴性受试者中表现不同的基因。一个简单的方法学正在开发，需要最低限度的频率或贝叶斯建模假设，并提供了两个efficientselection的非空的情况下，和估计的效果大小。在经典术语中，评估规模和功效。这种方法依赖于通过经验贝叶斯技术实现的错误发现率计算。一个典型的结果可能会报告“在10，000个基因中，有200个基因可以被清楚地鉴定为两组受试者之间的差异表达，但还有大约800个其他的非无效基因，这个实验没有足够的能力检测到。“经典的世纪统计理论是用来处理小问题的，几十个或几百个数据点，只有一个或几个未知参数。世纪的科学技术现在提供了大量的数据集，有数百万个单独的测量结果和数千个参数需要同时考虑。微阵列是最好的例子，但类似的问题也出现在各种各样的设备上：蛋白质组芯片、离光时间光谱学、流式细胞术和功能磁共振成像扫描仪。本研究的目标是一个有效的，计算效率高的方法analyzingmassive同时测试问题，而不需要extensivemodelling assumption.Monte Carlo方法在概率和统计（Persi Diaconis）本次调查的主要重点是统计计算的Monte Carlo和马尔可夫链算法的收敛速度。一个方面是相变（截止现象），扩展了Diaconis最近对Peres猜想的解决方案（与Saloff Coste联合）。工作包括使用计算工具，如Grobnerbases和组合特征，如Tuttes f-因子创建新的算法。这也有助于贝叶斯方法研究马尔可夫链，非参数和计算工具的先验分布。最后一个重点是在非标准的情况下，如unipotent群和Hecke代数的群论特征理论的发展。概率模型是现代科学研究的许多领域的基础，但它们提出了令人困惑的和重要的问题，关于模型与真实的世界现象的联系。迪亚康尼斯研究的是一些基础性的话题，比如“抛硬币是随机的”是什么意思？最近，这一发现（与苏珊·霍姆斯和理查德·蒙哥马利联合发现）表明，实际上，自然人类的硬币翻转会显示出一个很小但很重要的偏差（大约51%的结果与前一次相同）。仔细研究“随机性”的假设、合理性和有效性适用于广泛使用的模拟方法（算法应该运行多长时间才能完成任务？）。天气预报和空气污染只是需要这种模拟可靠性的两个领域。