Rational Kriging

This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimator of the mean from rational kriging is much more well behaved than that of ordinary kriging. Parameter estimation and uncertainty quantification for rational kriging are proposed using a Gaussian process framework. A generalized version of rational kriging is also proposed, which includes ordinary and rational kriging as special cases. Extensive simulations carried out over a wide class of functions show that the generalized rational kriging performs on par or better than both ordinary and rational kriging in terms of prediction and uncertainty quantification. The only extra step needed for generalized rational kriging over ordinary kriging is the computation of Perron eigenvector of an augmented correlation matrix which can be computed in near linear time and therefore, its overall computational complexity is no more than that of ordinary kriging. The potential applications of the new kriging methods in the emulation of computationally expensive models and model calibration problems are illustrated with real and simulated examples.