Statistical Theory and Methodology

统计理论与方法

• 批准号: 0804324
• 负责人: Bradley Efron
• 金额: $ 49.42万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0804324&HistoricalAwards=false
• 关键词: Statistical; Theory; Methodology

The investigators consider a class of problems in probability and statistical inference arising from large-scale scientific investigations. Massive hypothesis testing situations, with tens or hundreds of thousands of cases to consider simultaneously, are treated using empirical Bayes methods, as an efficient compromise between frequentist and Bayesian analyses. In a microarray experiment, for example, an empirical Bayes False Discovery Rate approach helps sift through thousands of z-values when searching for those genes of significant interest. Special attention if given to the appropriate choice of the null hypothesis, which may be quite different than classical text-book recipes. Markov chain monte carlo tech- niques are analyzed using eigen decompositions of the transition matrix to quantify how quickly initial conditions dissipate as the sampling algorithm proceeds toward steady state. Advanced applications involve implementing random sampling over curved manifolds in high-dimensional spaces.The general theme of this project is the development of mathematical methods of genuine practical utility, both in probability and statistical inference. Classical statistical methods were developed in a scientific world of small data sets investigating individual questions. Modern scientific technology, like microarrays, fMRI devices, and satellite imagers, now produce enormous data sets that aim to simultaneously investigate thousands of possibilities. This project proposes methods for dealing with the new scientific environment. New techniques of statistical inference and probabilistic modelling are proposed, based on recent experience in the biological, social science, and physical science worlds.

研究人员考虑了大规模科学调查中出现的一类概率和统计推断问题。大量的假设检验情况，有数万或数十万个案例要同时考虑，使用经验贝叶斯方法处理，作为频率分析和贝叶斯分析之间的有效折衷。例如，在微阵列实验中，经验贝叶斯错误发现率方法有助于在搜索显著感兴趣的基因时筛选数千个z值。如果给予适当的零假设选择，则要特别注意，这可能与经典教科书食谱截然不同。用转移矩阵的特征分解来分析马尔可夫链蒙特卡罗技术，以量化采样算法向稳定状态前进时初始条件消散的速度。高级应用包括在高维空间的曲线流形上实现随机抽样。这个项目的总主题是发展真正实用的数学方法，包括概率和统计推断。经典统计学方法是在研究个别问题的小数据集的科学世界中发展起来的。现代科学技术，如微阵列、功能磁共振成像设备和卫星成像仪，现在产生了旨在同时调查数千种可能性的海量数据集。这个项目提出了应对新的科学环境的方法。基于生物、社会科学和物理科学领域的最新经验，提出了统计推断和概率建模的新技术。