generate_predictive_mean_cov: A C++ function to generate predictive mean and cholesky...

In RobustGaSP: Robust Gaussian Stochastic Process Emulation

A C++ function to generate predictive mean and cholesky decomposition of the scaled covariance function.

Description

The function computes predictive mean and cholesky decomposition of the scaled covariance function.

Usage

generate_predictive_mean_cov(beta, nu, input, X,zero_mean,output,  
testing_input,X_testing, L, LX, theta_hat, sigma2_hat,rr0,r0, 
kernel_type,alpha,method,sample_data)

Arguments

beta	inverse-range parameters.
nu	noise-variance ratio parameter.
input	input matrix.
X	the mean basis function i.e. the trend function.
zero_mean	The mean basis function is zero or not.
output	output matrix.
testing_input	testing input matrix.
X_testing	mean/trend matrix of testing inputs.
L	a lower triangular matrix for the cholesky decomposition of R, the correlation matrix.
LX	a lower triangular matrix for the cholesky decomposition of $X^tR^-1X$. X^tR^{-1}X
theta_hat	estimated mean/trend parameters.
sigma2_hat	estimated variance parameter.
rr0	a matrix of absolute difference between testing inputs and testing inputs.
r0	a matrix of absolute difference between inputs and testing inputs.
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.
method	method of parameter estimation. post_mode means the marginal posterior mode is used for estimation. mle means the maximum likelihood estimation is used. mmle means the maximum marginal likelihood estimation is used. The post_mode is the default method.
sample_data	a boolean value. If true, the data (which may contain noise) is sampled. If false, the the mean of the data is sampled.

Value

A list of 2 elements. The first is a vector for predictive mean for testing inputs. The second is a scaled covariance matrix of the predictive distribution.

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.

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