neg_log_marginal_post_approx_ref_deriv: 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

Description

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

Usage

neg_log_marginal_post_approx_ref_deriv(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 vector.
CL	Pseudoparameter in the approximate reference prior.
a	Pseudoparameter in the approximate reference prior.
b	Pseudoparameter in the approximate reference prior.
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.

Value

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

Author(s)

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

Maintainer: Mengyang Gu <[e-mail]>

References

Mengyang 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.

RobustGaSP documentation built on May 29, 2024, 1:26 a.m.