dBvm

constBvm

Evaluation of the bivariate Sine von Mises density and its
normalizing constant.

Implementation of statistical methods for the estimation of
toroidal diffusions. Several diffusive models are provided, most of them
belonging to the Langevin family of diffusions on the torus. Specifically,
the wrapped normal and von Mises processes are included, which can be seen
as toroidal analogues of the Ornstein-Uhlenbeck diffusion. A collection of
methods for approximate maximum likelihood estimation, organized in four
blocks, is given: (i) based on the exact transition probability density,
obtained as the numerical solution to the Fokker-Plank equation; (ii) based
on wrapped pseudo-likelihoods; (iii) based on specific analytic
approximations by wrapped processes; (iv) based on maximum likelihood of
the stationary densities. The package allows the replicability of the
results in García-Portugués et al. (2019) <doi:10.1007/s11222-017-9790-2>.

Eduardo Portugues

sdetorus

Statistical Tools for Toroidal Diffusions

Eduardo García-Portugués

dBvm function

<dl><dt>x</dt>
<dd>a matrix of size <code>c(nx, 2)</code> for evaluating the density.</dd>
<dt>mu</dt>
<dd>two-dimensional vector of circular means.</dd>
<dt>kappa</dt>
<dd>three-dimensional vector with concentrations
\((\kappa_1, \kappa_2, \lambda)\).</dd>
<dt>logConst</dt>
<dd>logarithm of the normalizing constant. Computed if
<code>NULL</code>.</dd>
<dt>M</dt>
<dd>number of terms considered in the series expansion used for
evaluating the normalizing constant.</dd></dl>

Arguments

Bivariate Sine von Mises density — dBvm

<dl>

<dt>x</dt>
<dd>a matrix of size <code>c(nx, 2)</code> for evaluating the density.</dd>


<dt>mu</dt>
<dd>two-dimensional vector of circular means.</dd>


<dt>kappa</dt>
<dd>three-dimensional vector with concentrations
\((\kappa_1, \kappa_2, \lambda)\).</dd>


<dt>logConst</dt>
<dd>logarithm of the normalizing constant. Computed if
<code>NULL</code>.</dd>


<dt>M</dt>
<dd>number of terms considered in the series expansion used for
evaluating the normalizing constant.</dd>

</dl>

dBvm: Bivariate Sine von Mises density

Description

Usage

Value

Arguments

Details

References

Examples