TAG: Transformed Additive Gaussian Process

In TAG: Transformed Additive Gaussian Processes

Description

This function fits the Transformed Additive Gaussian (TAG) process.

Usage

TAG(iniTAG, HighD = FALSE, delta.threshold = -6)

Arguments

iniTAG	object of class inheriting from "initial.TAG".
HighD	logical. If TRUE, only κ and delta will be estimated. This is useful for high dimensional data. Default is False.
delta.threshold	the minimum value of log10(delta). Default is -6.

Details

The details of the TAG process can be found in Lin and Joseph (2019).

When HighD = FALSE, the weight parameters, the length scale parameters, the nugget parameter, and the Box-Cox transformation parameter are estimated. When HighD = TRUE, the length scale parameters for TAG is η*s0, where s0 is the initial estimate of the length scale parameters. Only η and the nugget parameter are estimated.

Value

The values returned from the function is a list containing the following components:

omega	The estimates of the weight parameters.
s	The estimates of the length scale parameters.
lambda	The estimate of the Box-Cox transformation parameter.
delta	The estimate of the nugget parameter in log10 scale. For example, delta = -6 means that the estimate of the nugget is 10^(-6).
kappa	If HighD is true, an estimate of kappa will be returned, which is a multiplication factor for the initial estimates of the length scale parameters.
ty	The transformed response vector.
X	The n by p input design matrix.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

See Also

initial.TAG for finding the initial values for the parameters in a TAG process, and pred.TAG for prediction.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)

TAG documentation built on June 8, 2021, 1:06 a.m.