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…