Predict {GPM}

The Prediction Function of GPM Package

Description

Predicts the reponse(s), associated prediction uncertainties, and gradient(s) of the GP model fitted by Fit.

Usage

Predict(XF, Model, MSE_on = 0, YgF_on = 0, grad_dim = rep(1, ncol(XF)))

Arguments

XF

Matrix containing the locations (settings) where the predictions are desired. The rows and columns of XF denote individual observation settings and input dimension, respectively.

Model

The GP model fitted by Fit.

MSE_on

Flag (a scalar) indicating whether the uncertainty (i.e., mean squared error MSE) associated with prediction of the response(s) should be calculated. Set to a non-zero value to calculate MSE.

YgF_on

Flag (a scalar) indicating whether the gradient(s) of the response(s) are desired. Set to a non-zero value to calculate the gradient(s). See note below.

grad_dim

A binary vector of length ncol(XF). The gradient of the response(s) will be calculated along the dimensions where the corresponding element of grad_dim is 1. grad_dim is ignored if YgF_on == 0.

Value

Output A list containing the following components:

• YF A matrix with n rows (the number of prediction points) and dy columns (the number of responses).

• MSE A matrix with n rows and dy columns where each element represents the prediction uncertainty (i.e., the expected value of the squared difference between the prediction and the true response) associated with the corresponding element in YF.

• YgF An array of size n by sum{grad_dim} by dx.

Note

1. The gradient(s) can be calculated if CorrType='G' or CorrType='LBG'. If CorrType='PE' or CorrType='LB', the gradient(s) can only be calculated if Power = 2 and Gamma = 1, respectively.

2. For efficiency, make sure the inputs are vecotrized and then passed to Predict. Avoid passing inputs individually in a for loop.

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.
Draw to plot the response via the fitted model.

Examples

# See the examples in the fitting function.