matern | R Documentation |
This function computes the Matérn correlation function given a distance matrix. The Matérn correlation function is given by
C(h)=\frac{2^{1-\nu}}{\Gamma(\nu)} \left(\frac{h}{\phi} \right)^{\nu}
\mathcal{K}_{\nu}\left( \frac{h}{\phi} \right),
where \phi
is the range parameter. \nu
is the smoothness parameter.
\mathcal{K}_{\nu}(\cdot)
is the modified Bessel function of the second kind of order \nu
.
The form of covariance includes the following special cases by specifying \nu
to be 0.5, 1.5, 2.5.
\nu=0.5
corresponds to the exponential correlation function (exp)
of the form
C(h) = \exp\left\{ - \frac{h}{\phi} \right\}
\nu=1.5
corresponds to the Matérn correlation function with smoothness parameter 1.5 (matern_3_2)
of the form
C(h) = \left( 1 + \frac{h}{\phi} \right) \exp\left\{ - \frac{h}{\phi} \right\}
\nu=2.5
corresponds to the Matérn correlation function with smoothness parameter 2.5 (matern_5_2)
of the form
C(h) = \left\{ 1 + \frac{h}{\phi} + \frac{1}{3}\left(\frac{h}{\phi}\right)^2 \right\} \exp\left\{ - \frac{h}{\phi} \right\}
matern(d, range, nu)
d |
a matrix of distances |
range |
a numerical value containing the range parameter |
nu |
a numerical value containing the smoothness parameter |
a numerical matrix
Pulong Ma mpulong@gmail.com
GPBayes-package, GaSP
, gp, CH
, kernel
, ikernel
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.