leaveOneOutVec.Kriging {rlibkriging}

Compute Leave-One-Out (LOO) vector error for an object with S3 class "Kriging" representing a kriging model.

Description

The returned value is the mean and stdev of \hat{y}_{i,(-i)}, the prediction of y_i based on the the observations y_j with j \neq i.

Usage

## S3 method for class 'Kriging'
leaveOneOutVec(object, theta, ...)

Arguments

object

A Kriging object.

theta

A numeric vector of range parameters at which the LOO will be evaluated.

...

Not used.

Value

The leave-One-Out vector computed for the given vector \boldsymbol{\theta} of correlation ranges.

Author(s)

Yann Richet [e-mail]

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(c(0.0, 0.25, 0.5, 0.75, 1.0))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2")
print(k)

x <- as.matrix(seq(0, 1, , 101))
p <- predict(k, x, TRUE, FALSE)

plot(f)
points(X, y)
lines(x, p$mean, col = 'blue')
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
        border = NA, col = rgb(0, 0, 1, 0.2))

# Compute leave-one-out (no range re-estimate) on 2nd point
X_no2 = X[-2,,drop=FALSE]
y_no2 = f(X_no2)
k_no2 = Kriging(y_no2, X_no2, "matern3_2", optim = "none", parameters = list(theta = k$theta()))
print(k_no2)

p_no2 <- predict(k_no2, x, TRUE, FALSE)
lines(x, p_no2$mean, col = 'red')
polygon(c(x, rev(x)), c(p_no2$mean - 2 * p_no2$stdev, rev(p_no2$mean + 2 * p_no2$stdev)), 
        border = NA, col = rgb(1, 0, 0, 0.2))

# Use leaveOneOutVec to get the same
loov = k$leaveOneOutVec(matrix(k$theta()))
points(X[2],loov$mean[2],col='red')
lines(rep(X[2],2),loov$mean[2]+2*c(-loov$stdev[2],loov$stdev[2]),col='red')