@article{3a35880d23ee4efd8581df0e2e77fa60,
title = "Postprocessing of MCMC",
abstract = "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.",
author = "South, {Leah F.} and Marina Riabiz and Onur Teymur and Oates, {Chris J.}",
note = "Funding Information: M.R., O.T., and C.J.O. were supported by the Lloyd{\textquoteright}s Register Foundation program on data-centric engineering at the Alan Turing Institute, United Kingdom. M.R. was supported by the British Heart Foundation—Alan Turing Institute cardiovascular data science award (BHF; SP/18/6/33805) and by the Wellcome/EPSRC Centre for Medical Engineering (WT203148/Z/16/Z). For the purpose of open access, the authors have applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission. The authors thank Matt Graham, Aki Vehtari, Ioannis Kontoyiannis, Pierre Jacob and an anonymous reviewer for helpful comments. Publisher Copyright: {\textcopyright} 2022 Annual Reviews Inc.. All rights reserved.",
year = "2022",
month = mar,
day = "1",
doi = "10.1146/annurev-statistics-040220-091727",
language = "English",
volume = "9",
pages = "529--555",
journal = "Annual Review of Statistics and Its Application",
issn = "2326-8298",
publisher = "Annual Reviews Inc.",
}