Automatically tuned general-purpose MCMC via new adaptive diagnostics

Adaptive Markov Chain Monte Carlo (MCMC) algorithms attempt to ‘learn’ from the results of past iterations so the Markov chain can converge quicker. Unfortunately, adaptive MCMC algorithms are no longer Markovian, so their convergence is difficult to guarantee. In this paper, we develop new diagnostics to determine whether the adaption is still improving the convergence. We present an algorithm which automatically stops adapting once it determines further adaption will not increase the convergence speed. Our algorithm allows the computer to tune a ‘good’ Markov chain through multiple phases of adaption, and then run conventional non-adaptive MCMC. In this way, the efficiency gains of adaptive MCMC can be obtained while still ensuring convergence to the target distribution.