Statistical Engineering Division
Seminar Series

Dr. William Notz
Ohio State University
Administration Building, Lecture Room C
November 4, 2004, 10:30-11:30 AM

In this talk I will discuss the design of computer experiments when there are two types of inputs: control variables and noise variables. Control variables are determined by a product designer while noise variables are uncontrolled in the field but take on values according to some probability distribution. I will consider two problems.  The first is the situation in which there are two outputs (responses), each of which is expensive or time consuming to compute.  The objective is to find values of the control variables that optimize the mean (over the distribution of the noise variables) of one response subject to a constraint on the mean of the other response. The second is to find values of the control variables at which the response is insensitive to the value of the noise variables.

For both problems, I will describe a sequential strategy to select the values of the inputs at which to observe the responses.  The methodology is Bayesian; the prior takes the responses as draws from a Gaussian stochastic process.  At each stage, the strategy determines which response to observe and at what set of inputs so as to maximize a posterior expected "improvement" over the current estimate of the optimum. This is joint work with Jeffrey Lehman, Tom Santner, and Brian Williams.