predict.CGP {CGP}

Predict from the composite Gaussian process model

Description

Compute predictions from the composite Gaussian process (CGP) model. 95% prediction intervals can also be calculated.

Usage

## S3 method for class 'CGP'
predict(object, newdata = NULL, PI = FALSE, ...)

Arguments

object

An object of class "CGP"

newdata

Optional. The matrix of predictive input locations, where each row of newdata corresponds to one predictive location

PI

If TRUE, 95% prediction intervals are also calculated. Default is FALSE

...

For compatibility with generic method predict

Details

Given an object of “CGP” class, this function predicts responses at unobserved newdata locations. If the PI is set to be TRUE, 95% predictions intervals are also computed.

If newdata is equal to the design matrix of the object, predictions from the CGP model will be identical to the yobs component of the object and the width of the prediction intervals will be shrunk to zero. This is due to the interpolating property of the predictor.

Value

The function returns a list containing the following components:

Yp

Vector of predictive values at newdata locations (Yp=gp+lp)

gp

Vector of predictive values at newdata locations from the global process

lp

Vector of predictive values at newdata locations from the local process

v

Vector of predictive standardized local volatilities at newdata locations

Y_low

If PI=TRUE, vector of 5% predictive quantiles at newdata locations

Y_up

If PI=TRUE, vector of 95% predictive quantiles at newdata locations

Author(s)

Shan Ba <[e-mail]> and V. Roshan Joseph <[e-mail]>

References

Ba, S. and V. Roshan Joseph (2012) “Composite Gaussian Process Models for Emulating Expensive Functions”. Annals of Applied Statistics, 6, 1838-1860.

See Also

CGP, print.CGP, summary.CGP

Examples

### A simulated example from Gramacy and Lee (2012) ``Cases for the nugget 
### in modeling computer experiments''. \emph{Statistics and Computing}, 22, 713-722.

#Training data
X<-c(0.775,0.83,0.85,1.05,1.272,1.335,1.365,1.45,1.639,1.675,
1.88,1.975,2.06,2.09,2.18,2.27,2.3,2.36,2.38,2.39)
yobs<-sin(10*pi*X)/(2*X)+(X-1)^4

#Testing data
UU<-seq(from=0.7,to=2.4,by=0.001)
y_true<-sin(10*pi*UU)/(2*UU)+(UU-1)^4

plot(UU,y_true,type="l",xlab="x",ylab="y")
points(X,yobs,col="red")
## Not run: 
#Fit the CGP model 
mod<-CGP(X,yobs)
summary(mod)

mod$objval
#-40.17315
mod$lambda
#0.01877432
mod$theta
#2.43932
mod$alpha
#578.0898
mod$bandwidth
#1
mod$rmscv
#0.3035192

#Predict for the testing data 'UU'
modpred<-predict(mod,UU)

#Plot the fitted CGP model
#Red: final predictor; Blue: global trend
lines(UU,modpred$Yp,col="red",lty=3,lwd=2)
lines(UU,modpred$gp,col="blue",lty=5,lwd=1.8)

## End(Not run)