Bayesian Analysis in Computer Experiments

• Activity Number: 227
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Stella W. Karuri*+
• Companies: University of Waterloo
• Keywords: computer experiments ; Bayesian analysis

Abstract

Mathematical models are commonly used in science and industry to simulate complex physical processes. These models are implemented by complex and expensive (in terms of run time) computer codes, limiting the number of simulation runs. A typical computer experiment involves running the code at a set of predetermined input levels to obtain a set of outputs. To analyze and obtain inference from the resulting output sets, the output is treated as a Gaussian stochastic process, a response surface is then fitted to the code. We outline a Bayesian formulation to this approach, prior uncertainty of the mean output, the variance and correlation between input is specified by means of the Jeffrey's prior. The Jeffrey's Prior appeal is that it results in a proper posterior. Using a Gaussian correlation structure, we approximate the Jeffreys Prior on log-transformed correlation parameters with a uniform prior. The approximation method results in a posterior that is easier to approximate and cheaper to compute. Comparisons using MCMC show that the approximation provides fairly similar results in predictions.