A Bayesian approach to the design and analysis of computational experiments
Toby J. Mitchell, Morris · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1988
In a computational experiment, the data are produced by a computer program that models a physical system. The experiment consists of a set of model runs; the design of the experiment specifies the choice of program inputs for each run. This paper centers on the problem of prediction (interpolation), the goal of which is to devise a design/analysis method which will provide predictions of model output for input values not run. We adopt a Bayesian approach as the basis for the analysis. Uncertainty about the response function is quantified by choosing a class of probability distributions over the function space. This leads to design procedures based on maximizing the expected reduction in ''amount of uncertainty,'' where the latter can be defined formally in terms of properties of the posterior distribution. Here we use as a design optimality criterion the determinant of the posterior covariance matrix of the responses at the input configurations at which we want to make predictions. This requires maximization of the determinant of the prior covariance matrix of the responses at the design sites. We describe our computer algorithm for constructing optimal designs, and give some examples of designs that it produces. 9 refs., 1 fig., 1more » tab.« less