IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-020-00236-x.html
   My bibliography  Save this article

Stick-Breaking processes, Clumping, and Markov Chain Occupation Laws

Author

Listed:
  • Zach Dietz

    (University of Arizona)

  • William Lippitt

    (University of Arizona)

  • Sunder Sethuraman

    (University of Arizona)

Abstract

We connect the empirical or ‘occupation’ laws of certain discrete space time-inhomogeneous Markov chains, related to simulated annealing, to a novel class of ‘stick-breaking’ processes, a ‘nonexchangeable’ generalization of the Dirichlet process used in nonparametric Bayesian statistics. To make this unexpected correspondence, we examine an intermediate ‘clumped’ structure in both the time-inhomogeneous Markov chains and the stick-breaking processes, perhaps of its own interest, which records the sequence of different states visited and the scaled proportions of time spent on them. By matching the associated intermediate structures, we identify the limits of the empirical measures of the time-inhomogeneous Markov chains as types of stick-breaking processes.

Suggested Citation

  • Zach Dietz & William Lippitt & Sunder Sethuraman, 2023. "Stick-Breaking processes, Clumping, and Markov Chain Occupation Laws," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 129-171, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-020-00236-x
    DOI: 10.1007/s13171-020-00236-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-020-00236-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-020-00236-x?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Günter Last, 2020. "An Integral Characterization of the Dirichlet Process," Journal of Theoretical Probability, Springer, vol. 33(2), pages 918-930, June.
    2. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, January.
    3. Gantert, Nina, 1990. "Laws of large numbers for the annealing algorithm," Stochastic Processes and their Applications, Elsevier, vol. 35(2), pages 309-313, August.
    Full references (including those not matched with items on IDEAS)

    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. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
    2. Laura Liu & Hyungsik Roger Moon & Frank Schorfheide, 2023. "Forecasting with a panel Tobit model," Quantitative Economics, Econometric Society, vol. 14(1), pages 117-159, January.
    3. A Stefano Caria & Grant Gordon & Maximilian Kasy & Simon Quinn & Soha Osman Shami & Alexander Teytelboym, 2024. "An Adaptive Targeted Field Experiment: Job Search Assistance for Refugees in Jordan," Journal of the European Economic Association, European Economic Association, vol. 22(2), pages 781-836.
    4. Miclo, Laurent, 1995. "Remarques sur l'ergodicité des algorithmes de recuit simulé sur un graphe," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 329-360, August.
    5. Martin Burda & Remi Daviet, 2023. "Hamiltonian sequential Monte Carlo with application to consumer choice behavior," Econometric Reviews, Taylor & Francis Journals, vol. 42(1), pages 54-77, January.
    6. Agustín G. Nogales, 2022. "On Consistency of the Bayes Estimator of the Density," Mathematics, MDPI, vol. 10(4), pages 1-6, February.
    7. Minerva Mukhopadhyay & Didong Li & David B. Dunson, 2020. "Estimating densities with non‐linear support by using Fisher–Gaussian kernels," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1249-1271, December.
    8. Meier, Alexander & Kirch, Claudia & Meyer, Renate, 2020. "Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    9. I. Votsi & G. Gayraud & V. S. Barbu & N. Limnios, 2021. "Hypotheses testing and posterior concentration rates for semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 707-732, October.
    10. Dmitry B. Rokhlin, 2020. "Relative utility bounds for empirically optimal portfolios," Papers 2006.05204, arXiv.org.
    11. János Engländer & Stanislav Volkov, 2018. "Turning a Coin over Instead of Tossing It," Journal of Theoretical Probability, Springer, vol. 31(2), pages 1097-1118, June.
    12. Sergei Seleznev, 2019. "Truncated priors for tempered hierarchical Dirichlet process vector autoregression," Bank of Russia Working Paper Series wps47, Bank of Russia.
    13. Moyu Liao, 2024. "Robust Bayesian Method for Refutable Models," Papers 2401.04512, arXiv.org, revised Sep 2024.
    14. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2024. "Semiparametric Bayesian Difference-in-Differences," Papers 2412.04605, arXiv.org, revised Dec 2024.
    15. Christopher D. Walker, 2023. "Parametrization, Prior Independence, and the Semiparametric Bernstein-von Mises Theorem for the Partially Linear Model," Papers 2306.03816, arXiv.org, revised Feb 2024.
    16. Walker, Stephen G., 2023. "Comparing weak and strong convergence of density functions," Statistics & Probability Letters, Elsevier, vol. 200(C).
    17. Petrova, Katerina, 2022. "Asymptotically valid Bayesian inference in the presence of distributional misspecification in VAR models," Journal of Econometrics, Elsevier, vol. 230(1), pages 154-182.
    18. Shota Gugushvili & Ester Mariucci & Frank van der Meulen, 2020. "Decompounding discrete distributions: A nonparametric Bayesian approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 464-492, June.
    19. Kaplan, David M. & Zhuo, Longhao, 2021. "Frequentist properties of Bayesian inequality tests," Journal of Econometrics, Elsevier, vol. 221(1), pages 312-336.
    20. Kawakami, Hajime, 2023. "Doob’s consistency of a non-Bayesian updating process," Statistics & Probability Letters, Elsevier, vol. 203(C).

    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:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-020-00236-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.