Sequential design of Gaussian process surrogates using pre-posterior analysis and Bayesian model averaging

Abstract

To build a surrogate model from experimental data ﾖ from tests or computer simulations ﾖ numerous options may exist when choosing a mathematical form. This is true for Gaussian Processes (GP) models, which may or may not include a regression basis ﾖ or mean trend ﾖ and be built on different correlation structures ﾖ through the selected covariance kernel. When data is scarce and prior information on the modeled phenomena is poor, it may be difficult to come to a conclusion on important decisions such as model selection or model improvement. If additional experimental information can be collected, often at significant cost, it is interesting to carry out model selection sequentially and efficiently. In this paper, we propose to leverage the ability of GPs to provide probabilistic descriptions and use it to look for the next ﾓbestﾔ point in the design space using a pre-posterior analysis scheme, or Value Of Information (VoI) evaluation. At such point, we expect to get the most relevant information, when the aim is to reduce expected prediction error, given a previous state of knowledge on the likelihood of various modeling options, e.g. using the idea of Bayesian Model Averaging (BMA). With successive queried points, we update our respective beliefs in these options through an ﾓinformation-optimalﾔ exploration of the design space ﾖ given current expectations according to priors. Hence, we attempt to learn efficiently both model structure and parameters.