generatePP

Generates one realization of an inhomogeneous Poisson process (PP) with given intensity function (using the thinning method).

Stochastic block model used for dynamic graphs represented by Poisson processes.
To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous Poisson process with intensity driven by the individuals’ latent groups. The model is shown to be identifiable and its estimation is based on a semiparametric variational expectation-maximization algorithm. Two versions of the method are developed, using either a nonparametric histogram approach (with an adaptive choice of the partition size) or kernel intensity estimators. The number of latent groups can be selected by an integrated classification likelihood criterion.
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C. Matias, T. Rebafka and F. Villers (2018). <doi:10.1093/biomet/asy016>.
C. Matias and S. Robin (2014). <doi:10.1051/proc/201447004>.
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P. Reynaud-Bouret (2006). <doi:10.3150/bj/1155735930>.

Daphnc3<a9> Giorgi

ppsbm

Clustering in Longitudinal Networks

Daphné Giorgi

Catherine Matias

Tabea Rebafka

Fanny Villers

generatePP function

<dl><dt>intens</dt>
<dd>Intensity function defined on [0,Time] (needs to be positive).</dd>
<dt>Time</dt>
<dd>Positive real number. [0,Time] is the total time interval of observation.</dd>
<dt>max.intens</dt>
<dd>Positive real number. Upper bound of intensity on [0,Time].</dd></dl>

Arguments

Poisson process generator — generatePP

<dl>

<dt>intens</dt>
<dd>Intensity function defined on [0,Time] (needs to be positive).</dd>


<dt>Time</dt>
<dd>Positive real number. [0,Time] is the total time interval of observation.</dd>


<dt>max.intens</dt>
<dd>Positive real number. Upper bound of intensity on [0,Time].</dd>

</dl>

generatePP: Poisson process generator

Description

Usage

Value

Arguments

Examples