Update_R_inv_y: Update the inverse of covariance multiplied by the outputs in...

In RobustCalibration: Robust Calibration of Imperfect Mathematical Models

Update the inverse of covariance multiplied by the outputs in the S-GaSP model.

Description

This function update the inverse of R_z multiple the outputs in the S-GaSP model for prediction.

Usage

Update_R_inv_y(R_inv_y,  R0,  beta_delta,   kernel_type,  alpha,  lambda_z,  num_obs)

Arguments

R_inv_y	A vector of inverse of covariance multiplied by the outputs.
R0	A List of matrix where the j-th matrix is an absolute difference matrix of the j-th input vector.
beta_delta	Inverse range parameters.
kernel_type	Type of kernel. matern_3_2 and matern_5_2 are Matern kernel with roughness parameter 3/2 and 5/2 respectively. pow_exp is power exponential kernel with roughness parameter alpha. If pow_exp is to be used, one needs to specify its roughness parameter alpha.
alpha	Roughness parameters in the kernel functions. It is only useful if the power exponential correlation function is used.
lambda_z	A parameter controling how close the math model to the reality in squared distance.
num_obs	Number of observations.

Value

A vector of the inverse of covariance multiplied by the outputs in the S-GaSP model.

Author(s)

Mengyang Gu [aut, cre]

Maintainer: Mengyang Gu <[e-mail]>

References

A. O'Hagan and M. C. Kennedy (2001), Bayesian calibration of computer models, Journal of the Royal Statistical Society: Series B (Statistical Methodology, 63, 425-464.

Mengyang Gu. (2016). Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output. Ph.D. thesis. Duke University.

M. Gu and L. Wang (2017) Scaled Gaussian Stochastic Process for Computer Model Calibration and Prediction. arXiv preprint arXiv:1707.08215.

RobustCalibration documentation built on Sept. 8, 2023, 5:23 p.m.