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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
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    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. 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.
    3. 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).
    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.
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    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).

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