Computing Equipment to Support Research in Statistics

这笔赠款将支持为四个需要大量密集计算的研究项目购买高性能计算设备。在“动态可靠性和几乎不变的数值”一书中，研究人员将为随机动态系统开发评估从状态空间的“良好”区域到故障区域的出口分布的方法。在计算上，这个问题涉及统计模拟、多参数优化、计算控制和计算几何。在“探索强调可视化的海量数据集”中，研究人员将开发预处理方法来获得多分辨率、索引简化的数据，这些数据可以在实时、交互式的可视化数据挖掘工具中进行探索。在“多重处理时间过程微阵列实验”中，研究人员将使用计算密集的重采样技术，以获得一种强大而强大的方法来识别生物感兴趣的基因。在《复杂抽样调查中的方差估计及相关问题》一书中，研究人员将研究在复杂设计下应用于回归估计器的重抽样方法和贝叶斯估计方法。《动态可靠性和几乎不变的数值》将提供计算复杂系统(如输电和通信网络)以及生物系统的故障概率的方法。“以可视化为重点的海量数据集的探索”将为大型数据集开发动态图形工具，这些工具将能够检测异常、罕见特征和难以使用数值程序检测的趋势的常见偏差。这些方法将应用于从气候监测、全球土地利用研究、绘制天空图和欺诈性网络活动中收集的数据。“多重处理时间-过程微阵列实验”将开发统计方法，以提高生物研究人员发现基因功能和了解基因如何共同作用进行基本生物过程的能力。在《复杂抽样调查中的方差估计及相关问题》一书中，研究人员将开发量化调查不确定性的方法，在这些调查中，传统的方差估计方法是不可行的。应用程序包括美国自然资源保护局的国家资源清单和美国人口普查局进行的当前人口调查。

This grant will support the purchase of high-performance computing equipment for four research projects that require large amounts of intensive computing. In "Numerics for Dynamical Reliability and Almost Invariance," the investigators will develop methods for evaluating exit distributions from "good" regions of the state space to failure regions, for random dynamical systems. Computationally, this problem involves statistical simulation, multi-parameter optimization, computational control, and computational geometry. In "Exploration of Massive Data Sets with Emphasis on Visualization," the investigators will develop pre-processing methods to obtain multi-resolution, indexed reduced data, that can be explored in a real-time, interactive visual data mining tool. In "Multiple-Treatment Time-Course Microarray Experiments," the investigator will use computationally intensive resampling techniques to obtain a robust and powerful method for identifying genes of biological interest. In "Variance Estimation and Related Problems in Complex Sample Surveys," the investigators will investigate the use of resampling methods and Bayesian methods of variance estimation, applied to regression estimators under complex designs."Numerics for Dynamical Reliability and Almost Invariance" will provide methods for computing failure probabilities of complicated systems like power transmission and communications networks, as well as biological systems. "Exploration of Massive Data Sets with Emphasis on Visualization," will develop dynamic graphics tools for large datasets that will be capable of detecting anomalies, rare features, and usual deviations from trends that are difficult to detect using numerical procedures. The methods will be applied to data collected from climate monitoring, global land use studies, mapping the sky, and fraudulent network activity. "Multiple-Treatment Time-Course Microarray Experiments" will develop statistical methods to enhance the ability of biological researchers to discover the functions of genes and to understand how genes act together to carry out essential biological processes. In "Variance Estimation and Related Problems in Complex Sample Surveys," the investigators will develop methods for quantifying uncertainty in surveys in which traditional variance estimation approaches are not practical. Applications include the National Resources Inventory of the US Natural Resources Conservation Service and the Current Population Survey, conducted by US Census Bureau.