Mathematical Sciences: Statistifcal Theory and Methodology

该项目的总体目标是开发 统计理论，可能直接用于 统计从业人员。 制定具体项目 围绕计算机密集型统计推断的主题。 专题包括引导，刀切及相关 再分配方法、置换检验和群论检验 程序，吉布斯抽样和马尔可夫链。 所有这些主题 关注统计人员特别感兴趣的数据映射。 历史上，排列是第一个研究的映射。 像bootstrap这样的方法将排列推广到更宽的 类的统计问题，以较少的代价 数学上的整洁和更大的计算开销。 这 该项目探讨了克服这些障碍的方法。 统计推断是从 观察到的数据，往往只是一个小的数量，以较大的 数据所来自的人群。 基本原则 统计推断的基本原理是在第二次世界大战前制定的。 的 基本理论是建立在古典数学和贝尔- 形曲线。 计算机密集型的方法，在过去的 15年来，旨在扩大范围，易用性和可扩展性， 统计参数。 他们用专门研制的 经典数学近似的计算机算法 与钟形曲线有关。 我们的研究旨在证明 这些算法。 数学和计算参数是 用于表明算法自动产生 经典的答案，当这样的答案存在，仍然给好 在更常见的情况下， 没有经典解。

The general goal of this project is the development of statistical theory that is likely to be of direct use to statistical practitioners. Specific projects are developed around the theme of computer-intensive statistical inference. Special topics include bootstrap, jackknife and related resampling methods, permutation tests and group theoretic testing procedures, Gibbs sampling and Markov chains. All these topics concern data mappings of special interest to statisticians. Historically, permutations were the first such mappings studied. Methods like the bootstrap generalize permutations to wider classes of statistical problems, at the expense of less mathematical neatness and greater computational expense. This project addresses ways to overcome these obstacles. Statistical inference is the science of generalization from observed data, often just a small amount, to the larger population from which the data were drawn. The basic principles of statistical inference were laid down before World War II. The basic theory was built around classical mathematics and the bell- shaped curve. Computer-intensive methods, developed in the last 15 years, aim to extend the range, ease, and plausibility of statistical arguments. They substitute specially-developed computer algorithms of classical mathematical approximations relating to the bell-shaped curve. Our research aims to justify these algorithms. Mathematical and computational arguments are used to show that the algorithms automatically produce the classical answers when such answers exist, and still give good answers in the much more common circumstance of problems having no classical solution.