Statistical Theory and Methodology

统计理论和方法这个项目的长期目标是为科学推理开发有用的工具，包括概率和统计。目前的建议侧重于概率分布的指数族，特别是当它们适用于复杂的应用，如图形模型和高维贝叶斯/频率计算。具体项目包括图形的指数族，包括协变量信息的影响，以及使用频率主义者自举计算贝叶斯推理分布的方法。指数族包括大多数众所周知的概率分布——二项分布、泊松分布、正态分布等，因此指数族结果具有广泛的应用范围。它们是应用统计学和理论统计学的核心，在概率论中也越来越重要。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，使用指数族结构来简化对所涉及的大量数据集的分析。贝叶斯理论的应用在“大数据”世界中越来越流行，本文将从自举（一种频率设备）的角度进行研究，目的是将这两种方法联系起来。

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.