TAG {TAG}

Transformed Additive Gaussian Process

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 \kappa 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 \eta*s0, where s0 is the initial estimate of the length scale parameters. Only \eta 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)