update_z_q0

Model-based clustering of multivariate continuous data using Bayesian mixtures of factor analyzers (Papastamoulis (2019) <DOI:10.1007/s11222-019-09891-z> (2018) <DOI:10.1016/j.csda.2018.03.007>). The number of clusters is estimated using overfitting mixture models (Rousseau and Mengersen (2011) <DOI:10.1111/j.1467-9868.2011.00781.x>): suitable prior assumptions ensure that asymptotically the extra components will have zero posterior weight, therefore, the inference is based on the ``alive'' components. A Gibbs sampler is implemented in order to (approximately) sample from the posterior distribution of the overfitting mixture. A prior parallel tempering scheme is also available, which allows to run multiple parallel chains with different prior distributions on the mixture weights. These chains run in parallel and can swap states using a Metropolis-Hastings move. Eight different parameterizations give rise to parsimonious representations of the covariance per cluster (following Mc Nicholas and Murphy (2008) <DOI:10.1007/s11222-008-9056-0>). The model parameterization and number of factors is selected according to the Bayesian Information Criterion. Identifiability issues related to label switching are dealt by post-processing the simulated output with the Equivalence Classes Representatives algorithm (Papastamoulis and Iliopoulos (2010) <DOI:10.1198/jcgs.2010.09008>, Papastamoulis (2016) <DOI:10.18637/jss.v069.c01>).

Panagiotis Papastamoulis

fabMix

Overfitting Bayesian Mixtures of Factor Analyzers with
Parsimonious Covariance and Unknown Number of Components

update_z_q0 function

<dl> <dt>w</dt>
<dd>Mixture weights</dd> <dt>mu</dt>
<dd>Marginal means</dd> <dt>SigmaINV</dt>
<dd>Precision matrix per component</dd> <dt>K</dt>
<dd>Number of components</dd> <dt>x_data</dt>
<dd>Data</dd></dl>

Arguments

Author

Gibbs sampling for \(z\) for \(q=0\) — update_z_q0

<dl>

 <dt>w</dt>
<dd>Mixture weights</dd>

 <dt>mu</dt>
<dd>Marginal means</dd>

 <dt>SigmaINV</dt>
<dd>Precision matrix per component</dd>

 <dt>K</dt>
<dd>Number of components</dd>

 <dt>x_data</dt>
<dd>Data</dd>

</dl>

update_z_q0: Gibbs sampling for \(z\) for \(q=0\)

Description

Usage

Value

Arguments

Author