White Noise Covariance Function

Computes the white noise covariance function: $$k(s, t) = \sigma^2 \mathbf{1}_{s = t}$$

Usage

kernel.whitenoise(variance = 1)

Arguments

variance

Variance (noise level) parameter \(\sigma^2\) (default 1).

Value

A covariance function object of class 'kernel_whitenoise'.

Details

where \(\mathbf{1}_{s = t}\) is 1 if \(s = t\) and 0 otherwise.

The white noise covariance function represents independent noise at each point. It can be added to other covariance functions to model observation noise.

See also

kernel.gaussian, make.gaussian.process

Examples

# White noise covariance produces independent samples at each point
cov_func <- kernel.whitenoise(variance = 0.1)
t <- seq(0, 1, length.out = 50)
K <- cov_func(t)
# K is diagonal