Postprocessing of MCMC

Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate posterior and derived quantities interest. Despite this, issue how output from a post-processed reported often overlooked. Convergence diagnostics can be control bias via burn-in removal, but these do not account for (common) situations where limited computational budget engenders bias-variance trade-off. The aim this article review state-of-the-art techniques post-processing output. Our covers methods based on discrepancy minimisation, which directly address trade-off, as well general-purpose variate approximating expected