A discussion on adaptive designs for computer experiments

Abstract

Maximum entropy sampling (MES) criteria provide a useful framework for studying sequential designs for computer experiments in a Bayesian framework. However, there is some technical difficulty in making the procedure fully adaptive in the sense of making proper use of previous output as well as input data. In the simple Gaussian set-up only previous input values need to be used. The approach discussed uses a full hierarchical model for the Gaussian process. The idea is to take advantage of the Karhumen-Loéve (K-L) expansion to approximate the process covariance function using an orthogonal function basis. It is argued that this may make it easier to use Bayesian hierarchical models, rather than estimating the covariance parameters directly, using the traditional approach. The article paper shows how to reduce the full MES method to a simple one by using a special empirical Bayes approximation, rather than using time-consuming integration. A simple simulator example is presented to show that full adaptation is beneficial.