Departmental Colloquium
Fred J. Hickernell
Illinois Institute of Technology
What are Good Designs?
Abstract: Laboratory experiments, computer experiments, and numerical
algorithms all require designs, i.e., the set of points where the
input function is evaluated. Unfortunately, in practice, the design
is not often given much thought. Grids aligned to the coordinate
axes are popular, but they become too costly as the number of
variables increases. Independent and identically distributed random
points allow one to overcome the curse of dimensionality, but they
usually lead to suboptimal answers. This talk describes several
families of good designs, such as orthogonal arrays, low discrepancy
points and minimax designs. For seemingly unrelated problems it is
found that a good design spreads points out evenly. Moreover, to
avoid the curse of dimensionality, low dimensional projections of the
design must also spread points evenly. The correct measures of even
spread are typically based on a distance or a reproducing kernel
(symmetric, positive definite matrix). This talk surveys known
results and poses open problems. No specialized background is
assumed, but the speaker intends to demonstrate how a variety of
ideas in mathematics, statistics, and computer science are needed to
construct and evaluate good designs.
Friday November 4, 2005 at 3:00 PM in SEO 636