edm_crit

Computes the distance in measure criterion.

Computes pseudo-realizations from the posterior distribution of a Gaussian Process (GP) with the method described in Azzimonti et al. (2016) <doi:10.1137/141000749>. The realizations are obtained from simulations of the field at few well chosen points that minimize the expected distance in measure between the true excursion set of the field and the approximate one. Also implements a R interface for (the main function of) Distance Transform of sampled Functions (<https://cs.brown.edu/people/pfelzens/dt/index.html>).

Dario Azzimonti

pGPx

Pseudo-Realizations for Gaussian Process Excursions

Julien Bect

Pedro Felzenszwalb

edm_crit function

<dl><dt>x</dt>
<dd>vector of dimension \(d\) representing the \(ith\) point where to compute the criterion</dd>
<dt>integration.points</dt>
<dd>p*d matrix of points for numerical integration in the X space.</dd>
<dt>integration.weights</dt>
<dd>Vector of size p corresponding to the weights of these integration points.</dd>
<dt>intpoints.oldmean</dt>
<dd>Vector of size p corresponding to the kriging mean at the integration points.</dd>
<dt>intpoints.oldsd</dt>
<dd>Vector of size p corresponding to the kriging standard deviation at the integration points.</dd>
<dt>precalc.data</dt>
<dd>list result of precomputeUpdateData with <code>model</code> and <code>x</code>.</dd>
<dt>model</dt>
<dd>km model</dd>
<dt>threshold</dt>
<dd>threshold selected for excursion set</dd>
<dt>batchsize</dt>
<dd>number of simulation points</dd>
<dt>alpha</dt>
<dd>value of Vorob'ev threshold</dd>
<dt>current.crit</dt>
<dd>Current value of the criterion</dd></dl>

Arguments

Distance in measure criterion — edm_crit

<dl>

<dt>x</dt>
<dd>vector of dimension \(d\) representing the \(ith\) point where to compute the criterion</dd>


<dt>integration.points</dt>
<dd>p*d matrix of points for numerical integration in the X space.</dd>


<dt>integration.weights</dt>
<dd>Vector of size p corresponding to the weights of these integration points.</dd>


<dt>intpoints.oldmean</dt>
<dd>Vector of size p corresponding to the kriging mean at the integration points.</dd>


<dt>intpoints.oldsd</dt>
<dd>Vector of size p corresponding to the kriging standard deviation at the integration points.</dd>


<dt>precalc.data</dt>
<dd>list result of precomputeUpdateData with <code>model</code> and <code>x</code>.</dd>


<dt>model</dt>
<dd>km model</dd>


<dt>threshold</dt>
<dd>threshold selected for excursion set</dd>


<dt>batchsize</dt>
<dd>number of simulation points</dd>


<dt>alpha</dt>
<dd>value of Vorob'ev threshold</dd>


<dt>current.crit</dt>
<dd>Current value of the criterion</dd>

</dl>

edm_crit: Distance in measure criterion

Description

Usage

Value

Arguments

References