IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v84y2022i4p1059-1081.html
   My bibliography  Save this article

Optimal thinning of MCMC output

Author

Listed:
  • Marina Riabiz
  • Wilson Ye Chen
  • Jon Cockayne
  • Pawel Swietach
  • Steven A. Niederer
  • Lester Mackey
  • Chris. J. Oates

Abstract

The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub‐optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to ‘burn in’ and removed, while the remainder of the chain is ‘thinned’ if compression is also required. In this paper, we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable when the gradient of the log‐target can be evaluated and approximation using a small number of states is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in Python, R and MATLAB.

Suggested Citation

  • Marina Riabiz & Wilson Ye Chen & Jon Cockayne & Pawel Swietach & Steven A. Niederer & Lester Mackey & Chris. J. Oates, 2022. "Optimal thinning of MCMC output," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1059-1081, September.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:4:p:1059-1081
    DOI: 10.1111/rssb.12503
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssb.12503
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssb.12503?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Chris J. Oates & Mark Girolami & Nicolas Chopin, 2017. "Control functionals for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 695-718, June.
    2. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    3. Michael A Colman, 2019. "Arrhythmia mechanisms and spontaneous calcium release: Bi-directional coupling between re-entrant and focal excitation," PLOS Computational Biology, Public Library of Science, vol. 15(8), pages 1-34, August.
    4. Takuo Matsubara & Jeremias Knoblauch & François‐Xavier Briol & Chris J. Oates, 2022. "Robust generalised Bayesian inference for intractable likelihoods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 997-1022, July.
    5. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hannaford, Naomi E. & Heaps, Sarah E. & Nye, Tom M.W. & Curtis, Thomas P. & Allen, Ben & Golightly, Andrew & Wilkinson, Darren J., 2023. "A sparse Bayesian hierarchical vector autoregressive model for microbial dynamics in a wastewater treatment plant," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    2. Dellaportas, Petros & Titsias, Michalis K. & Petrova, Katerina & Plataniotis, Anastasios, 2023. "Scalable inference for a full multivariate stochastic volatility model," Journal of Econometrics, Elsevier, vol. 232(2), pages 501-520.
    3. Kreuzer, Alexander & Dalla Valle, Luciana & Czado, Claudia, 2023. "Bayesian multivariate nonlinear state space copula models," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    4. Damien McParland & Szymon Baron & Sarah O’Rourke & Denis Dowling & Eamonn Ahearne & Andrew Parnell, 2019. "Prediction of tool-wear in turning of medical grade cobalt chromium molybdenum alloy (ASTM F75) using non-parametric Bayesian models," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1259-1270, March.
    5. Filippo Pagani & Martin Wiegand & Saralees Nadarajah, 2022. "An n‐dimensional Rosenbrock distribution for Markov chain Monte Carlo testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 657-680, June.
    6. Jair Andrade & Jim Duggan, 2021. "A Bayesian approach to calibrate system dynamics models using Hamiltonian Monte Carlo," System Dynamics Review, System Dynamics Society, vol. 37(4), pages 283-309, October.
    7. Ranjan, Rakesh & Sen, Rijji & Upadhyay, Satyanshu K., 2021. "Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    8. Ioannis Bournakis & Mike Tsionas, 2024. "A Non‐parametric Estimation of Productivity with Idiosyncratic and Aggregate Shocks: The Role of Research and Development (R&D) and Corporate Tax," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 641-671, June.
    9. Francis,David C. & Kubinec ,Robert, 2022. "Beyond Political Connections : A Measurement Model Approach to Estimating Firm-levelPolitical Influence in 41 Economies," Policy Research Working Paper Series 10119, The World Bank.
    10. Chen, Zhongfei & Wanke, Peter & Tsionas, Mike G., 2018. "Assessing the strategic fit of potential M&As in Chinese banking: A novel Bayesian stochastic frontier approach," Economic Modelling, Elsevier, vol. 73(C), pages 254-263.
    11. Martinovici, A., 2019. "Revealing attention - how eye movements predict brand choice and moment of choice," Other publications TiSEM 7dca38a5-9f78-4aee-bd81-c, Tilburg University, School of Economics and Management.
    12. Yongping Bao & Ludwig Danwitz & Fabian Dvorak & Sebastian Fehrler & Lars Hornuf & Hsuan Yu Lin & Bettina von Helversen, 2022. "Similarity and Consistency in Algorithm-Guided Exploration," CESifo Working Paper Series 10188, CESifo.
    13. Atkinson, Scott E. & Tsionas, Mike G., 2021. "Generalized estimation of productivity with multiple bad outputs: The importance of materials balance constraints," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1165-1186.
    14. Heinrich, Torsten & Yang, Jangho & Dai, Shuanping, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," MPRA Paper 105011, University Library of Munich, Germany.
    15. Caroline Khan & Mike G. Tsionas, 2021. "Constraints in models of production and cost via slack-based measures," Empirical Economics, Springer, vol. 61(6), pages 3347-3374, December.
    16. van Kesteren Erik-Jan & Bergkamp Tom, 2023. "Bayesian analysis of Formula One race results: disentangling driver skill and constructor advantage," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 19(4), pages 273-293, December.
    17. Jia Liu & John M. Maheu & Yong Song, 2024. "Identification and forecasting of bull and bear markets using multivariate returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 723-745, August.
    18. Dimitrakopoulos, Stefanos & Tsionas, Mike, 2019. "Ordinal-response GARCH models for transaction data: A forecasting exercise," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1273-1287.
    19. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    20. Belomestny, Denis & Goldman, Artur & Naumov, Alexey & Samsonov, Sergey, 2024. "Theoretical guarantees for neural control variates in MCMC," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 382-405.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:84:y:2022:i:4:p:1059-1081. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.