Log_marginal_post: Natural Logorithm of the posterior.

In RobustCalibration: Robust Calibration of Imperfect Mathematical Models

Natural Logorithm of the posterior.

Description

This function compute the natural Logorithm of the posterior assuming the GaSP or S-GaSP models for the discrepancy function.

Usage

Log_marginal_post(param, L_cur, output,  p_theta,  p_x, X, have_mean, CL, a, b,  cm_obs
,S_2_f,num_obs_all)

Arguments

param	Current parameters in the MCMC.
L_cur	Cholesky decomposition of the covariance matrix.
output	Experimental observations.
p_theta	Number of calibration parameters.
p_x	Number of range parameters.
X	Number of mean discrepancy parameters.
have_mean	Whether the mean discrepancy is zero or not.
CL	Prior parameter in the jointly robust prior.
a	Prior parameter in the jointly robust prior.
b	Prior parameter in the jointly robust prior.
cm_obs	Outputs from the mathematical model.
S_2_f	Variance of the data. This term is useful when there are repeated experiments.
num_obs_all	Total number of observations. If there is no repeated experiment, this is equal to the number of observable inputs.

Value

Natural logorithm of the posterior assuming the GaSP or S-GaSP models for the discrepancy function.

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.

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

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