## Gelman–Rubin convergence diagnostic using multiple chains

**Overview**

MCMC algorithms used for simulating posterior distributions are indispensable tools in Bayesian analysis. A major consideration in MCMC simulations is that of convergence. Has the simulated Markov chain fully explored the target posterior distribution so far, or do we need longer simulations? A common approach in assessing MCMC convergence is based on running and analyzing the difference between multiple chains.

For a given Bayesian model, **bayesmh** is capable of producing multiple Markov chains with randomly dispersed initial values by using the **initrandom** option, available as of the update on 19 May 2016. In this post, I demonstrate the Gelman–Rubin diagnostic as a more formal test for convergence using multiple chains. For graphical diagnostics, see *Graphical diagnostics using multiple chains* in **[BAYES] bayesmh** for more details. To compute the Gelman–Rubin diagnostic, I use an unofficial command, **grubin**, which can be installed by typing the following in Stata: Read more…