Sq_pitmanyor

Performs Bayesian nonparametric density estimation using Martingale
posterior distributions including the Copula Resampling (CopRe) algorithm.
Also included are a Gibbs sampler for the marginal Gibbs-type mixture model and
an extension to include full uncertainty quantification via a predictive
sequence resampling (SeqRe) algorithm. The CopRe and SeqRe samplers generate
random nonparametric distributions as output, leading to complete nonparametric
inference on posterior summaries. Routines for calculating arbitrary
functionals from the sampled distributions are included as well as an important
algorithm for finding the number and location of modes, which can then be used
to estimate the clusters in the data using, for example, k-means.
Implements work developed in Moya B., Walker S. G. (2022).
<doi:10.48550/arxiv.2206.08418>, Fong, E., Holmes, C., Walker, S. G. (2021)
<doi:10.48550/arxiv.2103.15671>, and Escobar M. D., West, M. (1995)
<doi:10.1080/01621459.1995.10476550>.

Blake Moya

copre

Tools for Nonparametric Martingale Posterior Sampling

The University of Texas at Austin 

Sq_pitmanyor function

<dl><dt>d</dt>
<dd>The discount parameter for the Pitman-Yor process. Must be less than
1.</dd>
<dt>alpha</dt>
<dd>The concentration parameter for the Pitman-Yor process. Must be
greater than -<code>sigma</code> if <code>sigma</code> is in [0, 1), else ignored.</dd>
<dt>m</dt>
<dd>A positive integer used to set <code>theta = m * abs(sigma)</code> if <code>sigma</code>
is negative.</dd></dl>

Arguments

Pitman-Yor Sequence Measure. — Sq_pitmanyor

<dl>

<dt>d</dt>
<dd>The discount parameter for the Pitman-Yor process. Must be less than
1.</dd>


<dt>alpha</dt>
<dd>The concentration parameter for the Pitman-Yor process. Must be
greater than -<code>sigma</code> if <code>sigma</code> is in [0, 1), else ignored.</dd>


<dt>m</dt>
<dd>A positive integer used to set <code>theta = m * abs(sigma)</code> if <code>sigma</code>
is negative.</dd>

</dl>

Sq_pitmanyor: Pitman-Yor Sequence Measure.

Description

Usage

Value

Arguments

See Also