rcalibration_MS-class | R Documentation |

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

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.

`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.

- predict_MS
See

`predict_MS`

.

Mengyang Gu [aut, cre]

Maintainer: Mengyang Gu <mengyang@pstat.ucsb.edu>

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.

`rcalibration_MS`

for more details about how to create a `rcalibration_MS`

object.

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