driftWn1D

Computes the drift of the WN diffusion in 1D in a vectorized way.

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

driftWn1D function

<dl><dt>x</dt>
<dd>a vector of length <code>n</code> containing angles. They all must be in \([\pi,\pi)\) so that the truncated wrapping by <code>maxK</code> windings is able to capture periodicity.</dd>
<dt>alpha</dt>
<dd>drift parameter.</dd>
<dt>mu</dt>
<dd>mean parameter. Must be in \([\pi,\pi)\).</dd>
<dt>sigma</dt>
<dd>diffusion coefficient.</dd>
<dt>maxK</dt>
<dd>maximum absolute value of the windings considered in the computation of the WN.</dd>
<dt>expTrc</dt>
<dd>truncation for exponential: <code>exp(x)</code> with <code>x &lt;= -expTrc</code> is set to zero. Defaults to <code>30</code>.</dd></dl>

Arguments

Drift of the WN diffusion in 1D — driftWn1D

<dl>

<dt>x</dt>
<dd>a vector of length <code>n</code> containing angles. They all must be in \([\pi,\pi)\) so that the truncated wrapping by <code>maxK</code> windings is able to capture periodicity.</dd>


<dt>alpha</dt>
<dd>drift parameter.</dd>


<dt>mu</dt>
<dd>mean parameter. Must be in \([\pi,\pi)\).</dd>


<dt>sigma</dt>
<dd>diffusion coefficient.</dd>


<dt>maxK</dt>
<dd>maximum absolute value of the windings considered in the computation of the WN.</dd>


<dt>expTrc</dt>
<dd>truncation for exponential: <code>exp(x)</code> with <code>x &lt;= -expTrc</code> is set to zero. Defaults to <code>30</code>.</dd>

</dl>

driftWn1D: Drift of the WN diffusion in 1D

Description

Usage

Value

Arguments

Examples