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