Statistical Theory and Methodology

翻译后摘要：该项目的目的是发展数理统计和概率的理论思想，这将是真正有用的科学从业者。 目前的建议涉及五个主要项目：详细研究马尔可夫链蒙特卡罗方法，特别是确定收敛速度的特征值理论; MCMC理论在截断数据中的应用;散点图平滑器的推理理论，包括自适应选择平滑器“窗口宽度”的竞争标准的相对效率，以及平滑器精度的适应成本;随机矩阵理论及其与Riemann zeta函数零点的联系;最后是提高Bootstrap置信区间精度的转换曲线方法。 这五个项目的连接主题是数学理论与计算机密集型算法的结合。

Abstract:This project aims to develop theoretical ideas in mathematical statistics and probability that will be of genuine use to scientific practitioners. The current proposal concerns five major projects: a detailed look at Markov Chain Monte Carlo methods, in particular the eigenvalue theory that determines rates of convergence; the application of MCMC theory to truncated data; inferential theory for scatterplot smoothers, including the relative efficiencies of competing criteria adaptively selecting the "window width" of the smoother, and also the cost of adaptation on the accuracy of the smoother; random matrix theory and its connection with the zeros of Riemann's zeta function; and finally conversion curve methods for improving the accuracy of bootstrap confidence intervals. The connecting theme for the five projects is the combination of mathematical theory with computer-intensive algorithms.