rphi2x

x2rphi

rtheta

dtheta

KLD10

theta2H

Functions for the mapping between spherical and
Euclidean coordinates.

Implement some models for
correlation/covariance matrices including two approaches
to model correlation matrices from a graphical structure.
One use latent parent variables as proposed in
Sterrantino et. al. (2024) <doi:10.48550/arXiv.2312.06289>.
The other uses a graph to specify conditional
relations between the variables.
The graphical structure makes correlation matrices
interpretable and avoids the quadratic increase of
parameters as a function of the dimension.
In the first approach a natural sequence of simpler
models along with a complexity penalization is used.
The second penalizes deviations from a base model.
These can be used as prior for model parameters,
considering C code through the 'cgeneric' interface
for the 'INLA' package (<https://www.r-inla.org>).
This allows one to use these models as building
blocks combined and to other latent Gaussian models
in order to build complex data models.

Elias Teixeira Krainski

graphpcor

Models for Correlation Matrices Based on Graphs

Elias Krainski

Denis Rustand

Anna Freni-Sterrantino

Janet van Niekerk

Haavard Rue’

rphi2x function

<dl><dt>rphi</dt>
<dd>numeric vector where the first element
is the radius and the remaining are the angles</dd>
<dt>x</dt>
<dd>parameters in the Euclidian space to be converted</dd>
<dt>n</dt>
<dd>integer to define the size of the correlation matrix</dd>
<dt>lambda</dt>
<dd>numeric as the parameter for the
Exponential distribution of the radius</dd>
<dt>R</dt>
<dd>scaling matrix (square root of the Hessian
around the base model)</dd>
<dt>theta.base</dt>
<dd>numeric vector of the base model</dd>
<dt>theta</dt>
<dd>numeric vector of length <code>m</code>.</dd>
<dt>H.elements</dt>
<dd>list output of theta2H</dd>
<dt>C1</dt>
<dd>is a correlation matrix.</dd>
<dt>C0</dt>
<dd>is a correlation matrix of the base model.</dd></dl>

Arguments

<ul>
<li><code>x2rphi()</code>: Tranform from Euclidian coordinates to spherical</li>
<li><code>rtheta()</code>: Drawn samples from the PC-prior for correlation</li>
<li><code>dtheta()</code>: PC-prior density for the correlation matrix</li>
<li><code>KLD10()</code>: Compute the KLD with respect to a base model</li>
<li><code>theta2H()</code>: Compute the hessian, its svd and some elements</li>
</ul>

Functions

Functions for the mapping between spherical and
Euclidean coordinates. — rphi2x

<dl>

<dt>rphi</dt>
<dd>numeric vector where the first element
is the radius and the remaining are the angles</dd>


<dt>x</dt>
<dd>parameters in the Euclidian space to be converted</dd>


<dt>n</dt>
<dd>integer to define the size of the correlation matrix</dd>


<dt>lambda</dt>
<dd>numeric as the parameter for the
Exponential distribution of the radius</dd>


<dt>R</dt>
<dd>scaling matrix (square root of the Hessian
around the base model)</dd>


<dt>theta.base</dt>
<dd>numeric vector of the base model</dd>


<dt>theta</dt>
<dd>numeric vector of length <code>m</code>.</dd>


<dt>H.elements</dt>
<dd>list output of theta2H</dd>


<dt>C1</dt>
<dd>is a correlation matrix.</dd>


<dt>C0</dt>
<dd>is a correlation matrix of the base model.</dd>

</dl>

rphi2x: Functions for the mapping between spherical and Euclidean coordinates.

Description

Usage

Arguments

Functions

Details