log_marginal_lik_deriv_ppgasp: Derivative of natural logarithm of the marginal likelihood

In RobustGaSP: Robust Gaussian Stochastic Process Emulation

Derivative of natural logarithm of the marginal likelihood

Description

The derivative of natural logarithm of marginal likelihood of the PP GaSP model with regard to inverse range parameters and nugget-variance ratio parameter after marginalizing out the mean (trend) and variance parameters by the location-scale prior. When the nugget is fixed, it only compute the derivative with regard to the inverse range parameter; otherwise it produces derivative with regard to inverse range parameter and nugget-variance ratio parameter.

Usage

log_marginal_lik_deriv_ppgasp(param, nugget, nugget_est, R0, X, zero_mean, 
output, 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	a matrix where each row is one runs of the computer model output.
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 numerical value of the derivative of natural logarithm of marginal likelihood with regard to range and nugget-variance ratio parameter (if not fixed). When the nugget is fixed, the derivative is on inverse-range parameters.

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.

See Also

log_marginal_lik_ppgasp.

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