Statistics Research

The main areas of theoretical statistical research in the Department of Statistics and OR are model selection procedures, multiple comparisons, nonparametric regression,  wavelets and their statistical applications, neural nets, and design of experiments.

A major research topic has been the "False Discovery  Rate" (FDR), a new and important idea in multiple comparisons. Several research projects are being carried out to study its properties and to extend its theoretical basis to model selection and other more general problems.

Nonparametric regression and  signal processing is another major research topic. In particular, the research focuses on applications of wavelets to various problems in nonparametric regression and signal de-noising. The optimality of wavelet-based de-noising procedures is being investigated. A Bayesian approach to wavelet de-noising is another topic of interest. This reserach is performed in collaboration with colleagues from Stanford University, University of Bristol,  University of Kent, Canterbury and others.

Applications of the FDR methodology to wavelet-based function estimation and signal de-noising procedures is also a current topic of major interest. Wavelet expansions involve a large number of coefficients to be estimated simultaneously and the FDR appears to be a highly successful method for identifying the truly important terms from the noisy ones.

Further research in nonparametric regression has considered various issues in spline smoothing.

Research on the use of neural nets has emphasized the use of  Bayesian statistics for analyzing data.

Much of the current research on design of experiments has been  directed toward industrial applications, stimulated by the "robust  design" experiments of G. Taguchi for improving the quality of products  and processes. Some of the topics include model based analysis of  cross-product array experiments, experiments for prototype development,  design and analysis of computer experiments and the use of a   hierarchical Bayesian model to effectively augment an initial  fractional factorial experiment.

Our theoretical interests have also found application in a   number of scientific collaborations. Wavelet methods have been  applied to develop automatic algorithms for "phase picking" from  noisy seismograms, an issue of importance to seismic monitoring of  the Comprehensive Test Ban Treaty. Ideas from optimal design of  experiments have been used to characterize optimal seismograph configurations for locating the source of seismic events.