Small sample Bayesian designs for complex high-dimensional models based on information gained using fast approximations.

Abstract

We consider the problem of designing for complex high-dimensional computer models that can be evaluated at different levels of accuracy. Ordinarily, this requires performing many expensive evaluations of the most accurate version of the computer model to obtain a reasonable coverage of the design space. In some cases, it is possible to supplement the information from the accurate model evaluations with a large number of evaluations of a cheap, approximate version of the computer model to enable a more informed design choice. We describe an approach that combines the information from both the approximate model and the accurate model into a single multiscale emulator for the computer model. We then propose a design strategy for selecting a small number of expensive evaluations of the accurate computer model based on our multiscale emulator and a decomposition of the input parameter space. We illustrate our methodology with an example concerning a computer simulation of a hydrocarbon reservoir.