Statistical Theory and Methodology

项目编号：DMS-050 5673 PI: Efron， Bradley and Diaconis， PersiNSF项目名称：统计学机构：斯坦福大学标题：统计理论与方法大规模同时测试（Bradley Efron）该研究员正在研究大规模同时假设测试情况的分析，例如微阵列实验寻找HIV阳性或阴性受试者中表现不同的基因。正在开发一种简单的方法，它需要最少的频率主义者或贝叶斯建模假设，并提供非零情况的有效选择和效应大小的估计。在经典术语中，大小和功率都要评估。这种方法依赖于错误发现率的计算，通过经验贝叶斯技术实现。一个典型的结果可能会报告“在10000个基因中，有200个可以被清楚地识别为两组受试者之间的差异表达，但还有大约800个其他非无效基因，这个实验还不够强大，无法检测到。”20世纪的经典统计理论是用来处理小问题的，几十或几百个数据点，有一个或几个未知参数。21世纪的科学技术现在提供了大量的数据集，可以同时考虑数百万个单独的测量结果和数千个参数。微阵列是主要的例子，但类似的问题也出现在各种各样的设备上：蛋白质组芯片、时间飞行光谱、流式细胞术和功能磁共振成像扫描仪。本研究的目标是一种高效的、计算效率高的方法，用于分析大规模同时测试问题，而不需要广泛的建模假设。概率与统计中的蒙特卡洛方法（Persi Diaconis）本研究的主要焦点是统计计算中蒙特卡洛马尔可夫链算法的收敛率。一个方面是相变（截止现象），扩展了Diaconis最近的Peres猜想解（与Saloff-Coste联合）。这项工作包括使用诸如grobnerbase之类的计算工具和诸如Tuttes f因子之类的组合表征来创建新的算法。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。最后的重点是在非标准情况下，如单幂群和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，但它们提出了关于模型与现实世界现象之间联系的令人困惑和重要的问题。Diaconis研究诸如“说掷硬币是随机的意味着什么”之类的基础主题？这导致了最近的发现（与苏珊·霍姆斯和理查德·蒙哥马利共同），事实上，自然的人类投掷硬币表现出一个小而显著的偏差（大约51%的人与前一次投掷相同）。仔细研究适用于广泛使用的模拟方法的“随机性”的假设、合理性和有效性（算法在完成工作之前应该运行多长时间？）天气预报和空气污染只是需要这种模拟的可靠性的两个领域。

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.