Statistical Theory and Methodology

摘要：本奖项主要研究领域包括：(1)基于马尔可夫链蒙特卡罗技术的大型稀疏列联表的精确方法；(2)基于Stein的方法改进经典正态展开和Edgeworth展开的精度；(3)使用专门设计的指数族进行密度估计和经验贝叶斯情况；(4)基于bootstrap的置信区间、似然分析和偏差校正技术的应用；(5)根据霍特林管公式计算同时测试情况下的常规长度和体积。这项研究的长期目标是将有前途的理论思想发展成对应用统计学家及其科学客户有直接价值的方法。这种形式的技术转让旨在利用新统计方法的范围和力量方面的最新发展。这里的思想属于“计算机密集型方法”的一般类别，这些方法利用现代计算机的能力将统计分析从经典数学可追溯性的界限中解放出来。这项研究并没有摒弃数学，而是利用数学来产生可以自动处理各种问题的统计工具。计算机密集的部分出现在统计消费者的水平上，计算取代了通常的正常理论近似和常规但困难的数学计算。

Proposal: DMS 95-04379 PI: Bradley Efron Institution: Stanford University Title: Statistical Theory and Methodology' ABSTRACT: The main research areas investigated under this award include: (1) Exact methods for large, sparse contingency tables based on Markov Chain Monte Carlo techniques; (2) Improvements on the accuracy of classical normal and Edgeworth expansions, based on Stein's method; (3) The use of specially designed exponential families for density estimation and empirical Bayes situations; (4) The application of bootstrap-based techniques for confidence intervals, likelihood analysis, and bias-correction; and (5) Length and volume calculations based on Hotelling's tube formula for routine use in simultaneous testing situations. The long-term goal of this research is the development of promising theoretical ideas into methodologies of direct value to applied statisticians and their scientific clients. This form of technology transfer aims to take advantage of current developments in the range and power of new statistical methodology. The ideas here fall into the general category of "computer-intensive methods", which are methods that take advantage of modern computer power to free statistical analysis from the bounds of classical mathematical tractability. The research does not banish mathematics, but uses mathematics to produce statistical tools that can work automatically on a wide variety of problems. The computer-intensive part comes in at the level of the statistical consumer, where computation is substituted for the usual normal theory approximations and routine but difficult mathematical computations.