Gaussian Process random generator

Generates n realizations of a zero-mean Gaussian process. The function also accepts user-defined covariance functions (without "nugget" effect, see cov), The implemented defaults with scale parameter \(\phi\), order \(o\) and nugget effect variance \(\sigma^2\) are:

squared exponential covariance \(Cov(x(t), x(t')) = \exp(-(t-t')^2)/\phi) + \sigma^2 \delta_{t}(t')\).
Wiener process covariance \(Cov(x(t), x(t')) = \min(t',t)/\phi + \sigma^2 \delta_{t}(t')\),
Matèrn process covariance \(Cov(x(t), x(t')) = \tfrac{2^{1-o}}{\Gamma(o)} (\tfrac{\sqrt{2o}|t-t'|}{\phi})^o \text{Bessel}_o(\tfrac{\sqrt{2o}|t-t'|}{s}) + \sigma^2 \delta_{t}(t')\)

Usage

tf_rgp(
  n,
  arg = 51L,
  cov = c("squareexp", "wiener", "matern"),
  scale = diff(range(arg))/10,
  nugget = scale/200,
  order = 1.5
)

Arguments

n: how many realizations to draw
arg: vector of evaluation points (arg of the return object). Defaults to (0, 0.02, 0.04, ..., 1). If given as a single integer (don't forget the L...), creates a regular grid of that length over (0,1).
cov: type of covariance function to use. Implemented defaults are "squareexp", "wiener", "matern", see Description. Can also be any vectorized function returning \(Cov(x(t), x(t'))\) without nugget effect for pairs of inputs t and t'.
scale: scale parameter (see Description). Defaults to the width of the domain divided by 10.
nugget: nugget effect for additional white noise / unstructured variability. Defaults to scale/200 (so: very little white noise).
order: order of the Matèrn covariance (if used, must be >0), defaults to 1.5. The higher, the smoother the process. Evaluation of the covariance function becomes numerically unstable for large (>20) order, use "squareexp".

Value

an tfd-vector of length n

Gaussian Process random generator

Usage

Arguments

Value

See also