Information Consistency of Stochastic Kriging and Its Implications

In this paper, we introduce the concept of information consistency for Bayesian Gaussian process models and further provide the information consistency results for stochastic kriging (SK). It is found that, to ensure information consistency of SK, the budget allocated should grow in a fashion that is commensurate with the smoothness level of the mean response function to estimate, as the number of design points approaches infinity. Moreover, it is recommended that an experiment design consist of a relatively large number of design points with a few replications at each when given a fixed budget to expend.