`Kriging::predict`

Description

Predict from a Kriging Model Object

Usage

Python

# k = Kriging(...)
k.predict(x, return_stdev = True, return_cov = False, return_deriv = False)

R

# k = Kriging(...)
k$predict(x, return_stdev = TRUE, return_cov = FALSE, return_deriv = FALSE)

Matlab/Octave

% k = Kriging(...)
k.predict(x, return_stdev = true, return_cov = false, return_deriv = false)

Julia

# k = Kriging(...)
p = predict(k, x, return_stdev=true, return_cov=false, return_deriv=false)
println(p.mean)
println(p.stdev)

Arguments

Argument	Description
`x`	Input points where the prediction must be computed.
`return_stdev`	`Logical` . If `TRUE` the standard deviation is returned.
`return_cov`	`Logical` . If `TRUE` the covariance matrix of the predictions is returned.
`return_deriv`	`Logical` . If `TRUE` the derivatives of mean and sd of the predictions are returned.

Details

Given \(n^\star\) “new” input points \(\mathbf{x}^\star_{j}\), the method compute the expectation, the standard deviation and (optionally) the covariance of the “new” observations \(y(\mathbf{x}^\star_j)\) of the stochastic process, conditional on the \(n\) values \(y(\mathbf{x}_i)\) at the input points \(\mathbf{x}_i\) as used when fitting the model. The \(n^\star\) input vectors (with length \(d\)) are given as the rows of a \(\mathbf{X}^\star\) corresponding to x.

The computation of these quantities is often called Universal Kriging see here for more details.

Value

A list containing the element mean and, depending on the requested flags, stdev, cov, mean_deriv, and stdev_deriv.

mean is the conditional expectation at the prediction inputs.
stdev is the vector of conditional standard deviations when return_stdev = TRUE.
cov is the conditional covariance matrix when return_cov = TRUE.
mean_deriv and stdev_deriv are the optional derivative matrices returned when return_deriv = TRUE.

For noise = NULL, prediction is an interpolation.

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
points(X, y, col = "blue", pch = 16)

k <- Kriging(y, X, "matern3_2")

x <-seq(from = 0, to = 1, length.out = 101)
p <- k$predict(x)

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))

Kriging::predict