Postprocessing of MCMC

Markov chain Monte Carlo is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is postprocessed and reported is often overlooked. Convergence diagnostics can be used to control bias via burn-in removal, but these do not account for (common) situations where a limited computational budget engenders a bias-variance trade-off. The aim of this article is to review state-of-the-art techniques for postprocessing Markov chain output. Our review covers methods based on discrepancy minimization, which directly address the bias-variance trade-off, as well as general-purpose control variate methods for approximating expected quantities of interest. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

ABE24: MHC Class I A*0201- GILGFVFTL-Vβ17Vα10.2 TCR complex: convergence diagnostics of internal energy

ABE24: MHC Class I A*0201- GILGFVFTL-Vβ17Vα10.2 TCR complex: convergence diagnostics of internal energy

ABD24: MHC Class I A*0201- GILGFVFTL-Vβ17Vα10.2 TCR complex: convergence diagnostics of number density

ABD24: MHC Class I A*0201- GILGFVFTL-Vβ17Vα10.2 TCR complex: convergence diagnostics of number density

ABD23: MHC Class I H-2Kbm3- EQYKFYSV-2C TCR complex: convergence diagnostics of number density

ABD23: MHC Class I H-2Kbm3- EQYKFYSV-2C TCR complex: convergence diagnostics of number density

ABE23: MHC Class I H-2Kbm3- EQYKFYSV-2C TCR complex: convergence diagnostics of internal energy

ABE23: MHC Class I H-2Kbm3- EQYKFYSV-2C TCR complex: convergence diagnostics of internal energy

ABE26: MHC Class I A*0201-LLFGYPRYV-A6 TCR complex: convergence diagnostics of internal energy

ABE26: MHC Class I A*0201-LLFGYPRYV-A6 TCR complex: convergence diagnostics of internal energy

ABE25: MHC Class I A*0201-LLFGYAVYV-A6 TCR complex: convergence diagnostics of internal energy

ABE25: MHC Class I A*0201-LLFGYAVYV-A6 TCR complex: convergence diagnostics of internal energy

ABE10: MHC Class I H-2Kb-INFDFNTI-BM3.3 TCR complex: convergence diagnostics of internal energy

ABE10: MHC Class I H-2Kb-INFDFNTI-BM3.3 TCR complex: convergence diagnostics of internal energy

MHC Class I A*0201-LLFGYPVYV-B7 TCR complex: convergence diagnostics of number density

MHC Class I A*0201-LLFGYPVYV-B7 TCR complexConvergence diagnostics of number density

MHC Class I A*0201-LLFGYPVYV-A6 TCR complex: convergence diagnostics of number density

MHC Class I A*0201-LLFGYPVYV-A6 TCR complexConvergence diagnostics of number density