safeSoftMax

Computes the weights \(w_i = \frac{e^{p_i}}{\sum_{j=1}^k e^{p_j}}\) from \(p_i\), \(i=1,\ldots,k\)
in a safe way to avoid overflows and to truncate automatically to zero low values of \(w_i\).

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

safeSoftMax function

<dl><dt>logs</dt>
<dd>matrix of logarithms where each row contains a set of \(p_1,\ldots,p_k\) to compute the weights from.</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

Safe softmax function for computing weights — safeSoftMax

<dl>

<dt>logs</dt>
<dd>matrix of logarithms where each row contains a set of \(p_1,\ldots,p_k\) to compute the weights from.</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>

safeSoftMax: Safe softmax function for computing weights

Description

Usage

Value

Arguments

Details

Examples