rcalibration_MS-class {RobustCalibration}

Robust Calibration for multiple sources class

Description

S4 class for multiple sources Robust rcalibration with or without the specification of the discrepancy model.

Objects from the Class

Objects of this class are created and initialized with the function rcalibration_MS that computes the prediction after calibrating the mathematical models from multiple sources.

Slots

num_sources:

Object of class integer. The number of sources.

p_x:

Object of class vector. Each element is the dimension of the observed inputs in each source.

p_theta:

Object of class integer. The number of calibration parameters.

num_obs:

Object of class vector.Each element is the number of experimental observations of each source.

index_theta:

Object of class list. The each element is a vector of the index of calibration parameters (theta) contained in each source.

input:

Object of class list. Each element is a matrix of the design of experiments in each source with dimension n_i x p_{x,i}, for i=1,...,num_sources.

output:

Object of class list. Each element is a vector of the experimental observations in each source with dimension n_i x 1, for i=1,...,num_sources.

X:

Object of class list. Each element is a matrix of the mean/trend discrepancy basis function in each source with dimension n_i x q_i, for i=1,...,num_sources.

have_trend:

Object of class vector. Each element is a bool to specify whether the mean/trend discrepancy is zero in each source. "TRUE" means it has zero mean discrepancy and "FALSE"" means the mean discrepancy is not zero.

q:

Object of class vector. Each element is integer of the number of basis functions of the mean/trend discrepancy in each source.

R0:

Object of class list. Each element is a list of matrices where the j-th matrix is an absolute difference matrix of the j-th input vector in each source.

kernel_type:

Object of class vector. Each element is a character to specify the type of kernel to use in each source.

alpha:

Object of class list. Each element is a vector of parameters for the roughness parameters in the kernel in each source.

theta_range:

A matrix for the range of the calibration parameters.

lambda_z:

Object of class vector. Each element is a numeric value about how close the math model to the reality in squared distance when the S-GaSP model is used for modeling the discrepancy in each source.

S:

Object of class integer about how many posterior samples to run.

S_0:

Object of class integer about the number of burn-in samples.

prior_par:

Object of class list. Each element is a vector about prior parameters.

output_weights:

Object of class list. Each element is a vector about the weights of the experimental data.

sd_proposal_theta:

Object of class vector about the standard deviation of the proposal distribution for the calibration parameters.

sd_proposal_cov_par:

Object of class list. Each element is a vector about the standard deviation of the proposal distribution for the calibration parameters in each source.

discrepancy_type:

Object of class vector. Each element is a character about the type of the discrepancy in each source. If it is 'no-discrepancy', it means no discrepancy function. If it is 'GaSP', it means the GaSP model for the discrepancy function. If it is 'S-GaSP', it means the S-GaSP model for the discrepancy function.

simul_type:

Object of class vector. Each element is an integer about the math model/simulator. If the simul_type is 0, it means we use RobustGaSP R package to build an emulator for emulation. If the simul_type is 1, it means the function of the math model is given by the user. When simul_type is 2 or 3, the mathematical model is the geophyiscal model for Kilauea Volcano. If the simul_type is 2, it means it is for the ascending mode InSAR data; if the simul_type is 3, it means it is for the descending mode InSAR data.

emulator_rgasp:

Object of class list. Each element is an S4 class of rgasp from the RobustGaSP package in each source.

emulator_ppgasp:

Object of class list. Each element is an S4 class of ppgasp from the RobustGaSP package in each source.

post_theta:

Object of class matrix for the posterior samples of the calibration parameters after burn-in.

post_individual_par:

Object of class list. Each element is a matrix for the posterior samples after burn-in in each source.

post_value:

Object of class vector for the posterior values after burn-in.

accept_S_theta:

Object of class numerical for the number of proposed samples of the calibration parameters are accepted in MCMC.

accept_S_beta:

Object of class vector for the number of proposed samples of the range and nugget parameters in each source are accepted in MCMC.

count_boundary:

Object of class vector for the number of proposed samples of the calibation parameters are outside the range and they are rejected directly.

have_measurement_bias_recorded:

Object of class bool for whether measurement bias will be recorded or not.

measurement_bias:

Object of class bool for whether measurement bias exists or not.

post_delta:

Object of class matrix of samples of model discrepancy.

post_measurement_bias:

Object of class list of samples of measurement_bias if measurement bias is chosen to be recorded.

thinning:

Object of class integer for the ratio between the number of posterior samples and the number of samples to be recorded.

emulator_type:

Object of class vector for the type of emulator for each source of data. 'rgasp' means scalar-valued emulator and 'ppgasp' means vectorized emulator.

loc_index_emulator:

Object of class list for location index to output in ghe ppgasp emulator for computer models with vectorized output.

Methods

predict_MS

See predict_MS.

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.

M. 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.

M. Gu (2018) Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection . arXiv preprint arXiv:1804.09329.

See Also

rcalibration_MS for more details about how to create a rcalibration_MS object.