Bayesian model averaging for Kriging regression structure selection

Abstract

Kriging metamodels are widely used to approximate the response of computationally-intensive engineering models for a variety of applications, ranging from system design to uncertainty quantification. Their predictions are formulated by combining a regression that captures global trends of the true model with a Gaussian process approximation that provides a localized correction. Conventional Kriging approaches construct the regression model with a single set of basis functions. Selection among different candidate sets of basis functions is typically deterministically performed, choosing a single model based on some optimality criterion, ignoring, therefore, any uncertainties in this identification. In this paper, a Bayesian model class averaging formulation is adopted to consider different sets of basis functions, and therefore different regression models in establishing the Kriging predictions. Each model is weighted by its respective posterior model probability when aggregating the final predictions. To enable the computationally efficient application of such a Bayesian model averaging scheme, a data-driven and tractable prior distribution is proposed, and multiple strategies in the inference and prediction stage are presented. Numerical examples show that the proposed Kriging implementation is capable of constructing a more accurate metamodel than other alternatives with comparable computational cost. Comparisons are performed with respect to both the mean metamodel predictions as well as to the predictions established within an uncertainty quantification setting.