mvn.gibbs

This function generates a Markov chain sample from a multivariate normal distribution using a two-block Gibbs sampler. The function is used mainly for implementation in the examples of this package.

Practitioners of Bayesian statistics often use Markov chain Monte Carlo (MCMC) samplers to sample from a posterior distribution. This package determines whether the MCMC sample is large enough to yield reliable estimates of the target distribution. In particular, this calculates a Gelman-Rubin convergence diagnostic using stable and consistent estimators of Monte Carlo variance. Additionally, this uses the connection between an MCMC sample's effective sample size and the Gelman-Rubin diagnostic to produce a threshold for terminating MCMC simulation. Finally, this informs the user whether enough samples have been collected and (if necessary) estimates the number of samples needed for a desired level of accuracy. The theory underlying these methods can be found in "Revisiting the Gelman-Rubin Diagnostic" by Vats and Knudson (2018) <arXiv:1812:09384>.

Christina Knudson

stableGR

A Stable Gelman-Rubin Diagnostic for Markov Chain Monte Carlo

Dootika Vats

mvn.gibbs function

<dl><dt>N</dt>
<dd>number of Markov chain samples desired</dd>
<dt>p</dt>
<dd>dimension of the multivariate normal target distribution</dd>
<dt>mu</dt>
<dd>mean vector of the multivariate normal distribution</dd>
<dt>sigma</dt>
<dd>covariance matrix of the multivariate normal distribution</dd></dl>

Arguments

Two block Gibbs sampler for a multivariate normal distribution — mvn.gibbs

<dl>

<dt>N</dt>
<dd>number of Markov chain samples desired</dd>


<dt>p</dt>
<dd>dimension of the multivariate normal target distribution</dd>


<dt>mu</dt>
<dd>mean vector of the multivariate normal distribution</dd>


<dt>sigma</dt>
<dd>covariance matrix of the multivariate normal distribution</dd>

</dl>

mvn.gibbs: Two block Gibbs sampler for a multivariate normal distribution

Description

Usage

Value

Arguments