### Archive

Posts Tagged ‘multiple chains’

## Bayesian inference using multiple Markov chains

Overview

Markov chain Monte Carlo (MCMC) is the principal tool for performing Bayesian inference. MCMC is a stochastic procedure that utilizes Markov chains simulated from the posterior distribution of model parameters to compute posterior summaries and make predictions. Given its stochastic nature and dependence on initial values, verifying Markov chain convergence can be difficult—visual inspection of the trace and autocorrelation plots are often used. A more formal method for checking convergence relies on simulating and comparing results from multiple Markov chains; see, for example, Gelman and Rubin (1992) and Gelman et al. (2013). Using multiple chains, rather than a single chain, makes diagnosing convergence easier.

As of Stata 16, bayesmh and its bayes prefix commands support a new option, nchains(), for simulating multiple Markov chains. There is also a new convergence diagnostic command, bayesstats grubin. All Bayesian postestimation commands now support multiple chains. In this blog post, I show you how to check MCMC convergence and improve your Bayesian inference using multiple chains through a series of examples. I also show you how to speed up your sampling by running multiple Markov chains in parallel. Read more…

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## Gelman–Rubin convergence diagnostic using multiple chains

As of Stata 16, see [BAYES] bayesstats grubin and Bayesian analysis: Gelman-Rubin convergence diagnostic.

The original blog posted May 26, 2016, omitted option initrandom from the bayesmh command. The code and the text of the blog entry were updated on August 9, 2018, to reflect this.

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…

Categories: Statistics Tags: