exponential_anisotropic2D

d_exponential_anisotropic2D

From a matrix of locations and covariance parameters of the form
(variance, L11, L21, L22, 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

exponential_anisotropic2D function

<dl><dt>covparms</dt>
<dd>A vector with covariance parameters
in the form (variance, L11, L21, L22, nugget)</dd>
<dt>locs</dt>
<dd>A matrix with <code>n</code> rows and <code>2</code> columns.
Each row of locs is a point in R^2.</dd></dl>

Arguments

<ul>
<li><code>d_exponential_anisotropic2D()</code>: Derivatives of anisotropic exponential covariance</li>
</ul>

Functions

The covariance parameter vector is (variance, L11, L21, L22, nugget)
where L11, L21, L22, are the three non-zero entries of a lower-triangular
matrix L. The covariances are 
$$ M(x,y) = \sigma^2 exp(-|| L x - L y || ) $$
This means that L11 is interpreted as an inverse range parameter in the
first dimension.
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

Geometrically anisotropic exponential covariance function (two dimensions) — exponential_anisotropic2D

<dl>

<dt>covparms</dt>
<dd>A vector with covariance parameters
in the form (variance, L11, L21, L22, nugget)</dd>


<dt>locs</dt>
<dd>A matrix with <code>n</code> rows and <code>2</code> columns.
Each row of locs is a point in R^2.</dd>

</dl>

The covariance parameter vector is (variance, L11, L21, L22, nugget)
where L11, L21, L22, are the three non-zero entries of a lower-triangular
matrix L. The covariances are 
$$ M(x,y) = \sigma^2 exp(-|| L x - L y || ) $$
This means that L11 is interpreted as an inverse range parameter in the
first dimension.
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 $.

exponential_anisotropic2D: Geometrically anisotropic exponential covariance function (two dimensions)

Description

Usage

Value

Arguments

Functions

Parameterization