NLogL {GPM}

The Function for calculating the Negative Log-Likelehood in GPM Package

Description

Calculates the negative log-likelihood (excluding all the constant terms) as described in reference 1.

Usage

NLogL(Omega, X, Y, CorrType, MinEig, Fn, n, dy)

Arguments

Omega

The vector storing all the hyperparameters of the correlation function. The length of Omega depends on the CorrType. See reference 1.

X

Matrix containing the training (aka design or input) data points. The rows and columns of X denote individual observation settings and input dimension, respectively.

Y

Matrix containing the output (aka response) data points. The rows and columns of Y denote individual observation responses and output dimension, respectively.

CorrType

The correlation function of the GP model. Choices include 'G' (default), 'PE', 'LBG', and 'LB'. See Fit and the references.

MinEig

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.

Fn

A matrix of 1's with nrow(X) rows and 1 column. See reference 1.

n

Number of observations, nrow(X).

dy

Number of responses, ncol(Y).

Details

Fit calls this function with scaled X and Y. That is, when the user fits a GP model by calling Fit(X, Y), X and Y are mapped to the [0, 1] region and then passed to this function.

Value

nlogl The negative log-likelihood (excluding all the constant terms). See the references.

References

1. 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.

2. Plumlee, M. & Apley, D. W. (2017) Lifted Brownian kriging models. Technometrics, 59, 165-177.

See Also

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.

Examples

# see the examples in the fitting function.