***PLEASE NOTE UNUSUAL DAY AND TIME***
Seminar Notice
Statistical Laboratory
Iowa State University
DATE AND TIME: Wednesday, May 4, 2005, 9:00 a.m.
PLACE: 319 Snedecor
SPEAKER: Curtis Miller, Department of Statistics, Iowa State University
TITLE: Search for Level Sets of Functions by Computer
Experiments
ABSTRACT
In engineering and other fields, it is common to use a computer simulation
to model a real world process. The inputs to a function f represent
factors that influence the outcome. The output represents a quantity of
interest. Often there will be a specified level L, and the objective
is to find the inputs for which output is above L. L may be a tolerance
level, and the inputs for which response is larger than L form a tolerance
region. We might estimate the tolerance region by evaluating f on a grid, but
even a coarse grid may have thousands of points in four or five
dimensions. If the function f is costly to evaluate, we need to be able to
estimate the tolerance region with as few evaluations as possible.
We approach this problem with a sequential search. Use data at any
stage to fit a spatial process that approximates the function. Fit a
Gaussian spatial process, as described in Currin, Mitchell, Morris, and
Ylvisaker[1991]. The spatial process gives an estimate of the
L-contour. We can also use the process to estimate how much information
would be gained if f is evaluated at point p. Choose points where it is
estimated that f takes value L, but where uncertainty is high. Evaluate f
at the chosen points. This will augment the set of data points and the
vector of data values. Repeat the procedure with this augmented data.
Calculate convergence criteria after each iteration, and stop when criteria
reach predetermined goals.
The search process is applied to several functions defined in low
dimensional space. Finally, it is applied to an actual simulation
function
COFFEE: 8:40 a.m., 104 Snedecor Hall
Jeanette La Grange
Department of Statistics
102 Snedecor
Iowa State University
Ames, IA 50010-1210
515 294-3440 (office)
515 294-4040 (fax)