base_measure

A structure for wrapping base measures as in Escobar and West
(1995).

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 

base_measure function

<dl><dt>idx</dt>
<dd>A unique index for the base measure.</dd>
<dt>dim</dt>
<dd>A dimension for the support of the base measure.</dd>
<dt>pars</dt>
<dd>A list of parameters used to generate mixture components.</dd>
<dt>hpars</dt>
<dd>A list of hyperparameters used to generate <code>pars</code>.</dd>
<dt>eval</dt>
<dd>An evaluation function taking <code>phi</code>, a list of mixture parameter
matrices, <code>grd</code>, a grid vector, <code>f</code>, a character string indicating whether
to calculate the gradient, density, or distribution function, and
<code>nthreads</code>, a number of threads to utilize for parallel execution.</dd></dl>

Arguments

Base Measure for Mixture Models — base_measure

<dl>

<dt>idx</dt>
<dd>A unique index for the base measure.</dd>


<dt>dim</dt>
<dd>A dimension for the support of the base measure.</dd>


<dt>pars</dt>
<dd>A list of parameters used to generate mixture components.</dd>


<dt>hpars</dt>
<dd>A list of hyperparameters used to generate <code>pars</code>.</dd>


<dt>eval</dt>
<dd>An evaluation function taking <code>phi</code>, a list of mixture parameter
matrices, <code>grd</code>, a grid vector, <code>f</code>, a character string indicating whether
to calculate the gradient, density, or distribution function, and
<code>nthreads</code>, a number of threads to utilize for parallel execution.</dd>

</dl>

base_measure: Base Measure for Mixture Models

Description

Usage

Value

Arguments

References

See Also