matern_scaledim

d_matern_scaledim

From a matrix of locations and covariance parameters of the form
(variance, range_1, ..., range_d, smoothness, nugget), return the square matrix of
all pairwise covariances.

Functions for fitting and doing predictions with
Gaussian process models using Vecchia's (1988) approximation.
Package also includes functions for reordering input locations,
finding ordered nearest neighbors (with help from 'FNN' package),
grouping operations, and conditional simulations.
Covariance functions for spatial and spatial-temporal data
on Euclidean domains and spheres are provided. The original
approximation is due to Vecchia (1988)
<http://www.jstor.org/stable/2345768>, and the reordering and
grouping methods are from Guinness (2018)
<doi:10.1080/00401706.2018.1437476>.
Model fitting employs a Fisher scoring algorithm described
in Guinness (2019) <doi:10.48550/arXiv.1905.08374>.

Joseph Guinness

GpGp

Fast Gaussian Process Computation Using Vecchia's Approximation

Matthias Katzfuss

Youssef Fahmy

matern_scaledim function

<dl><dt>covparms</dt>
<dd>A vector with covariance parameters
in the form (variance, range_1, ..., range_d, smoothness, nugget)</dd>
<dt>locs</dt>
<dd>A matrix with <code>n</code> rows and <code>d</code> columns.
Each row of locs is a point in R^d.</dd></dl>

Arguments

<ul>
<li><code>d_matern_scaledim()</code>: Derivatives with respect to parameters</li>
</ul>

Functions

The covariance parameter vector is (variance, range_1, ..., range_d, smoothness, nugget).
The covariance function is parameterized as
$$ M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (|| D^{-1}(x - y) || )^\nu K_\nu(|| D^{-1}(x - y) || ) $$
where D is a diagonal matrix with (range_1, ..., range_d) on the diagonals.
The nugget value $ \sigma^2 \tau^2 $ is added to the diagonal of the covariance matrix.
NOTE: the nugget is $ \sigma^2 \tau^2 $, not $ \tau^2 $.

Parameterization

Matern covariance function, different range parameter for each dimension — matern_scaledim

<dl>

<dt>covparms</dt>
<dd>A vector with covariance parameters
in the form (variance, range_1, ..., range_d, smoothness, nugget)</dd>


<dt>locs</dt>
<dd>A matrix with <code>n</code> rows and <code>d</code> columns.
Each row of locs is a point in R^d.</dd>

</dl>

The covariance parameter vector is (variance, range_1, ..., range_d, smoothness, nugget).
The covariance function is parameterized as
$$ M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (|| D^{-1}(x - y) || )^\nu K_\nu(|| D^{-1}(x - y) || ) $$
where D is a diagonal matrix with (range_1, ..., range_d) on the diagonals.
The nugget value $ \sigma^2 \tau^2 $ is added to the diagonal of the covariance matrix.
NOTE: the nugget is $ \sigma^2 \tau^2 $, not $ \tau^2 $.

matern_scaledim: Matern covariance function, different range parameter for each dimension

Description

Usage

Value

Arguments

Functions

Parameterization