StickBreaking

piDirichlet

A Dirichlet process can be represented using a stick breaking construction
$$G = \sum _{i=1} ^n pi _i \delta _{\theta _i}$$,
where $\pi _k = \beta _k \prod _{k=1} ^{n-1} (1- \beta _k )$ are the stick breaking weights.
The atoms $\delta _{\theta _i}$ are drawn from $G_0$ the base measure of the Dirichlet Process.
The $\beta _k \sim \mathrm{Beta} (1, \alpha)$. In theory $n$ should be infinite, but we chose some value of $N$ to truncate
the series. For more details see reference.

Perform nonparametric Bayesian analysis using Dirichlet
processes without the need to program the inference algorithms.
Utilise included pre-built models or specify custom
models and allow the 'dirichletprocess' package to handle the
Markov chain Monte Carlo sampling.
Our Dirichlet process objects can act as building blocks for a variety
of statistical models including and not limited to: density estimation,
clustering and prior distributions in hierarchical models.
See Teh, Y. W. (2011)
<https://www.stats.ox.ac.uk/~teh/research/npbayes/Teh2010a.pdf>,
among many other sources.

Dean Markwick

dirichletprocess

Build Dirichlet Process Objects for Bayesian Modelling

Gordon J. Ross

Kees Mulder

Giovanni Sighinolfi

Filippo Fiocchi 

StickBreaking function

<dl><dt>alpha</dt>
<dd>Concentration parameter of the Dirichlet Process.</dd>
<dt>N</dt>
<dd>Truncation value.</dd>
<dt>betas</dt>
<dd>Draws from the Beta distribution.</dd></dl>

Arguments

<ul>
<li><code>piDirichlet()</code>: Function for calculating stick lengths.</li>
</ul>

Functions

The Stick Breaking representation of the Dirichlet process. — StickBreaking

<dl>

<dt>alpha</dt>
<dd>Concentration parameter of the Dirichlet Process.</dd>


<dt>N</dt>
<dd>Truncation value.</dd>


<dt>betas</dt>
<dd>Draws from the Beta distribution.</dd>

</dl>

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StickBreaking: The Stick Breaking representation of the Dirichlet process.

Description

Usage

Value

Arguments

Functions

References