neg_log_marginal_post_approx_ref_deriv_ppgasp: Derivative of negative natural logarithm of approximate...

In RobustGaSP: Robust Gaussian Stochastic Process Emulation

Derivative of negative natural logarithm of approximate reference marginal posterior density of the PP GaSP model

Description

The function computes the derivative (with regard to log of inverse range parameter) of natural logarithm of marginal posterior density of the PP GaSP model with the jointly robust prior after marginalizing out the mean (trend) and variance parameters by the location-scale prior.

Usage

neg_log_marginal_post_approx_ref_deriv_ppgasp(param, nugget, nugget.est, 
                                       R0, X, zero_mean,output, CL, a, b, 
                                      kernel_type, alpha)

Arguments

param	A vector of natural logarithm of inverse-range parameters and natural logarithm of the nugget-variance ratio parameter.
nugget	The nugget-variance ratio parameter if this parameter is fixed.
nugget.est	Boolean value of whether the nugget is estimated or fixed.
R0	A List of matrix where the j-th matrix is an absolute difference matrix of the j-th input vector.
X	The mean basis function i.e. the trend function.
zero_mean	The mean basis function is zero or not.
output	The output matrix.
CL	Pseudoparameter in the approximate reference prior.
a	Pseudoparameter in the approximate reference prior.
b	Pseudoparameter in the approximate reference prior.
kernel_type	A vector of integer specifying the type of kernels of each coordinate of the input. In each coordinate of the vector, 1 means the pow_exp kernel with roughness parameter specified in alpha; 2 means matern_3_2 kernel; 3 means matern_5_2 kernel; 5 means periodic_gauss kernel; 5 means periodic_exp kernel.
alpha	Roughness parameters in the kernel functions.

Value

The derivative of natural logarithm of marginal posterior density with the jointly robust prior.

Author(s)

Mengyang Gu [aut, cre], Jesus Palomo [aut], James Berger [aut]

Maintainer: Mengyang Gu <[e-mail]>

References

M. Gu. and J.O. Berger (2016). Parallel partial Gaussian process emulation for computer models with massive output. Annals of Applied Statistics, 10(3), 1317-1347.

M. Gu. (2016). Robust uncertainty quantification and scalable computation for computer models with massive output. Ph.D. thesis. Duke University.

M. Gu (2018), Jointly robust prior for Gaussian stochastic process in emulation, calibration and variable selection, arXiv:1804.09329.

See Also

neg_log_marginal_post_approx_ref_ppgasp.

RobustGaSP documentation built on June 1, 2022, 9:08 a.m.