Statistical Theory and Methodology

建议：DMS95-04379 PI：布拉德利·埃夫隆研究所：斯坦福大学题目：统计理论和方法论摘要：本奖项研究的主要领域包括：(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)基于斯坦方法的经典正态展开和埃奇沃斯展开式的精度改进；(3)使用专门设计的指数族进行密度估计和经验贝叶斯情形；(4)基于Bootstrap技术的置信度区间、似然分析和偏差校正的应用；以及(5)基于霍特林管公式的长度和体积计算，用于同时测试情况下的常规使用。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和他们的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目前在新统计方法的范围和力量方面的发展。这里的想法属于“计算机密集型方法”的一般范畴，这些方法利用现代计算机的能力，将统计分析从经典数学处理的界限中解放出来。这项研究并没有抛弃数学，而是使用数学来产生统计工具，这些工具可以自动处理各种各样的问题。计算机密集的部分来自统计消费者的层面，计算被通常的正态理论近似和常规但困难的数学计算所取代。

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.