Statistical Theory and Methodology

现代计算能力、现代理论和现代科学设备产生的扩展数据集极大地增加了统计推断的范围。这项研究项目调查了大规模数据收集中提出的一系列概率和统计问题。尽管经验贝叶斯方法的使用越来越多，但事实证明，它很难证明是合理的。该项目正在开发的方法将指数族理论的新应用带到了这项工作中，目的是澄清随着样本量的增加，经验贝叶斯分析如何收敛到传统的贝叶斯方法。该项目旨在开发使用大规模并行数据集的经验贝叶斯方法，例如来自微阵列研究的数据集，以改进在报告许多小型子实验的情况下的估计，每个子实验本身的精度都较低；以及改进的蒙特卡罗方法，用于计算机解决大规模优化问题。本研究项目中研究的具体主题包括大规模经验贝叶斯策略，在以前难以处理的情况下用于计算机辅助推理的重要性抽样，以及传统精度估计方法的稳定性评估理论。概率分布的指数族在计算和统计推断中都起着核心作用。在海量数据分析中使用它们的一个特别顽固的障碍是在指数族密度中缺乏合适的规范常数。这项研究项目进一步发展了基于适当变分问题的解的计算方法；一个有前途的应用是在图形模型领域。指数族的第二个应用包括对数据集进行有效的反卷积，以获得经验贝叶斯估计。

Modern computational capabilities, modern theory, and the expanded data sets produced by modern scientific equipment have greatly increased the scope of statistical inference. This research project investigates a set of questions in probability and statistics raised by large-scale data collection. While of increasing use, empirical Bayes methods have proved difficult to justify. The approach under development in this project brings a novel application of exponential family theory to the job, with the goal of clarifying how empirical Bayes analyses converge to traditional Bayes methods as sample sizes increase. The project aims to develop empirical Bayes methods that use large-scale parallel data sets, such as those from microarray studies, to improve estimation in situations reporting many small sub-experiments, each of which by itself has low accuracy; and improved Monte Carlo methods for the computer solution of massive optimization problems.Specific topics under investigation in this research project include large-scale empirical Bayes strategies, importance sampling for computer-assisted inference in formerly intractable situations, and a theory of stability assessment for traditional methods of accuracy estimation. Exponential families of probability distributions play a central role in both computation and statistical inference. A particularly stubborn impediment to their use in massive data analyses is the lack of a suitable norming constant in the exponential family density. This research project further develops computational methods based on solutions of appropriate variational problems; a promising application is in the area of graphical models. A second application of exponential families involves efficient deconvolution of datasets to obtain empirical Bayes estimates.