Postprocessing of MCMC
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Description
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.
Impact and interest:
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ID Code: | 234441 | ||
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Item Type: | Contribution to Journal (Review article) | ||
Refereed: | Yes | ||
ORCID iD: |
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Additional Information: | Acknowledgments: M.R., O.T., and C.J.O. were supported by the Lloyd'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. | ||
Measurements or Duration: | 27 pages | ||
DOI: | 10.1146/annurev-statistics-040220-091727 | ||
ISSN: | 2326-8298 | ||
Pure ID: | 113755333 | ||
Divisions: | Current > Research Centres > Centre for Data Science Current > QUT Faculties and Divisions > Faculty of Science Current > Schools > School of Mathematical Sciences |
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Funding Information: | M.R., O.T., and C.J.O. were supported by the Lloyd’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. | ||
Copyright Owner: | 2022 Annual Reviews Inc. | ||
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||
Deposited On: | 08 Aug 2022 06:01 | ||
Last Modified: | 18 Jul 2024 22:59 |
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