Statistical Theory and Methodology

统计理论和方法Persi Diaconis和布拉德利EfronThe长期目标的这个项目一直是发展有用的工具，科学推理，无论是在概率和统计。本建议侧重于指数族的概率分布，特别是当它们适用于复杂的应用程序，如图形模型和高维贝叶斯/频率计算。具体项目包括图的指数族，包括协变量信息的影响，以及如何使用频率自助法来计算贝叶斯推断分布。指数族包括大多数著名的概率分布-二项式，泊松，正态等-因此指数族结果具有广泛的应用范围。他们生活在应用和理论统计的核心，并在概率论中越来越重要。图形模型，包括对互联网、基因表达数据和社交网络（如Facebook）的研究，使用指数家族结构来简化对所涉及的巨大数据集的分析。贝叶斯应用的理论，越来越受欢迎的“大数据”的世界，在这里调查的引导程序，一个frequentist设备，连接两种方法的目标。

Statistical Theory and MethodologyPersi Diaconis and Bradley EfronThe long-term goal of this project has been the development of useful tools for scientific inference, both in probability and statistics. The present proposal focuses on exponential families of probability distributions, especially as they apply to complex applications such as graphical models and high-dimensional Bayesian/frequentist computation. Specific projects include exponential families for graphs, including the effects of covariate information, and ways of using the frequentist bootstrap to compute Bayesian inferential distributions.Exponential families include most of the well-known probability distributions -- binomial, Poisson, normal etc, -- so exponential family results have a wide scope of application. They live at the core of applied and theoretical statistics, and are of growing importance in probability theory. Graphical models, which include studies of the internet, gene expression data, and social networks such as Facebook, use exponential family structure to simplify analysis of the enormous data sets involved. Bayesian applications of the theory, increasingly popular in the "Big Data" world, are investigated here in terms of the bootstrap, a frequentist device, with the goal of connecting the two approaches.