A theoretical framework of the scaled Gaussian stochastic process in prediction and calibration. (arXiv:1807.03829v1 [math.ST])

The Gaussian stochastic process (GaSP) is a useful technique for predicting nonlinear outcomes. The estimated mean function in a GaSP, however, can be far from the reality in terms of the $L_2$ distance. This problem was widely observed in calibrating imperfect mathematical models using experimental data, when the discrepancy function is modeled as a GaSP. In this work, we study the theoretical properties of the scaled Gaussian stochastic process (S-GaSP), a new stochastic process to address the identifiability problem of the mean function in the GaSP model. The GaSP is a special case of the S-GaSP with the scaling parameter being zero. We establish the explicit connection between the GaSP and S-GaSP through the orthogonal series representation. We show the predictive mean estimator in the S-GaSP calibration model converges to the reality at the same rate as the GaSP with the suitable choice of the regularization parameter and scaling parameter. We also show the calibrated mathematical 查看全文>>