A practical sequential stopping rule for high-dimensional Markov chain Monte Carlo

To this end, we propose using an automated sequential stopping procedure that terminates the simulation when the computational uncertainty is small relative to the posterior uncertainty. Further, we show this stopping rule is equivalent to stopping when the effective sample size is sufficiently large.

Such a stopping rule has previously been shown to work well in settings with posteriors of moderate dimension. In this paper, we illustrate its utility in high-dimensional simulations while overcoming some current computational issues. As examples, we consider two complex Bayesian analyses on spatially and temporally correlated datasets.