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.
