Statistical Theory and Methodology

研究人员考虑了由大规模科学调查引起的概率和统计推断中的一类问题。大规模的假设检验情况，同时考虑数万或数十万个案例，使用经验贝叶斯方法处理，作为频率主义者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重要基因时筛选数千个z值。如果要特别注意零假设的适当选择，这可能与经典教科书的食谱大不相同。马尔可夫链蒙特卡罗技术分析使用转移矩阵的特征分解来量化如何快速初始条件耗散的采样算法的过程中，趋于稳定状态。高级应用包括在高维空间的弯曲流形上实现随机抽样。这个项目的总体主题是发展真正实用的数学方法，包括概率和统计推断。经典的统计方法是在小数据集调查个体问题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，现在产生了庞大的数据集，旨在同时调查数千种可能性。这个项目提出了应对新的科学环境的方法。基于最近在生物、社会科学和物理科学领域的经验，提出了统计推断和概率建模的新技术。

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.