Calculates some auxiliary paramters to obtain the negative log-likelehood and its gradient.
Auxil(Omega, X, Y, CorrType, MinEig, Fn, n, dy)
The vector storing all the hyperparameters of the correlation function. The length of Omega
depends on the CorrType
. See reference 1
.
Matrix containing the training (aka design or input) data points. The rows and columns of X
denote individual observation settings and input dimension, respectively.
Matrix containing the output (aka response) data points. The rows and columns of Y
denote individual observation responses and output dimension, respectively.
The correlation function of the GP model. Choices include 'G'
(default), 'PE'
, 'LBG'
, and 'LB'
. See Fit
and the references
.
The smallest eigen value that the correlation matrix is allowed to have, which in return determines the appraopriate nugget that should be added to the correlation matrix.
A matrix of 1
's with nrow(X)
rows and 1
column. See reference 1
.
Number of observations, nrow(X)
.
Number of responses, ncol(Y)
.
ALL A list containing the following components (based on CorrType
, some other parameters are also stored in ALL
):
R
The correlation matrix whose smallest eigen value is >= MinEig
.
L
Cholesky decomposition of R
.
Raw_MinEig
The smallest eigen value of R
before adding Nug_opt
.
Nug_opt
The added nugger to R
.
B
Since Auxil
is shared between NLogL
and NLogL_G
during optimization, ideally it should be run only once (e.g., via memoisation). Such an implementation is left for future editions.
Bostanabad, R., Kearney, T., Tao, S., Apley, D. W. & Chen, W. (2018) Leveraging the nugget parameter for efficient Gaussian process modeling. Int J Numer Meth Eng, 114, 501-516.
Plumlee, M. & Apley, D. W. (2017) Lifted Brownian kriging models. Technometrics, 59, 165-177.
Fit
to see how a GP model can be fitted to a training dataset.
Predict
to use the fitted GP model for prediction.
Draw
to plot the response via the fitted model.
# NOT RUN {
# see the examples in the fitting function.
# }
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