Department of Statistical Science
Duke University
presents:
Douglas Nychka
North Carolina State University
"Constructing Spatial Designs by Selecting Subsets or Filling Space"
Abstract: An important problem in spatial statistics is determining where to make measurements. For example, in monitoring environmental pollutants one would like to know how to place a network of measuring instruments to make most efficient use of resources. A basic model for observations is a Gaussian random field with an isotropic covariance function. Given this model there are simple estimators (kriging, BLUE) for predicting the field at locations where measurements are not taken. However, even under this homogeneous model choosing design points to minimize the prediction variance is difficult numerically and is not feasible for large numbers of observation points.
This work presents two strategies for constructing designs that are readily computable and offer the promise of interactive use. Given a set of candidate points it is shown that there is an equivalence between choosing an optimal subset for predicting the average and a regression subset selection problem. Besides using the exhaustive branch and bound algorithm for subset selection (in Splus the "leaps" function), a new method, the lasso, is also considered. The lasso is a recent development by Robert Tibshirani and is based on a regularization/Bayesian principle. These designs are compared to space-filling designs over a range of correlation functions. The results suggest that both designs based on subset selection are as good or better than a space filling criterion. The results are also applied to shrink an ozone monitoring network for the Chicago urban area.
Friday, October 27, 1995
11:45 - 12:45
116 Old Chemistry Building Any questions concerning the seminar may be addressed to Cheryl McGhee @ (919) 684-8029, e-mail cheryl@stat.duke.edu, or finger seminar@stat.duke.edu.