IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v208y2013i1d10.1007_s10479-012-1121-6.html
   My bibliography  Save this article

Asymptotically optimal Bayesian sequential change detection and identification rules

Author

Listed:
  • Savas Dayanik

    (Bilkent University)

  • Warren B. Powell

    (Princeton University)

  • Kazutoshi Yamazaki

    (Osaka University)

Abstract

We study the joint problem of sequential change detection and multiple hypothesis testing. Suppose that the common distribution of a sequence of i.i.d. random variables changes suddenly at some unobservable time to one of finitely many distinct alternatives, and one needs to both detect and identify the change at the earliest possible time. We propose computationally efficient sequential decision rules that are asymptotically either Bayes-optimal or optimal in a Bayesian fixed-error-probability formulation, as the unit detection delay cost or the misdiagnosis and false alarm probabilities go to zero, respectively. Numerical examples are provided to verify the asymptotic optimality and the speed of convergence.

Suggested Citation

  • Savas Dayanik & Warren B. Powell & Kazutoshi Yamazaki, 2013. "Asymptotically optimal Bayesian sequential change detection and identification rules," Annals of Operations Research, Springer, vol. 208(1), pages 337-370, September.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:d:10.1007_s10479-012-1121-6
    DOI: 10.1007/s10479-012-1121-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-012-1121-6
    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/s10479-012-1121-6?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. Apostolos N. Burnetas & Michael N. Katehakis, 1997. "Optimal Adaptive Policies for Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 222-255, February.
    2. Savas Dayanik & Christian Goulding & H. Vincent Poor, 2008. "Bayesian Sequential Change Diagnosis," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 475-496, May.
    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. Pergamenchtchikov, Serguei M. & Tartakovsky, Alexander G. & Spivak, Valentin S., 2022. "Minimax and pointwise sequential changepoint detection and identification for general stochastic models," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Savas Dayanik & Kazutoshi Yamazaki, 2022. "Detection and identification of changes of hidden Markov chains: asymptotic theory," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 261-301, July.

    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. Savas Dayanik & Warren Powell & Kazutoshi Yamazaki, 2013. "Asymptotically optimal Bayesian sequential change detection and identification rules," Annals of Operations Research, Springer, vol. 208(1), pages 337-370, September.
    2. Athanassios N. Avramidis & Arnoud V. Boer, 2021. "Dynamic pricing with finite price sets: a non-parametric approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 1-34, August.
    3. Lu, Zexian & Chen, Yunxiao & Li, Xiaoou, 2022. "Optimal parallel sequential change detection under generalized performance measures," LSE Research Online Documents on Economics 118348, London School of Economics and Political Science, LSE Library.
    4. Savas Dayanik & Kazutoshi Yamazaki, 2022. "Detection and identification of changes of hidden Markov chains: asymptotic theory," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 261-301, July.
    5. Michael Jong Kim, 2016. "Robust Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 64(4), pages 999-1014, August.
    6. Katehakis, Michael N. & Puranam, Kartikeya S., 2012. "On bidding for a fixed number of items in a sequence of auctions," European Journal of Operational Research, Elsevier, vol. 222(1), pages 76-84.
    7. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
    8. Warren B. Powell, 2016. "Perspectives of approximate dynamic programming," Annals of Operations Research, Springer, vol. 241(1), pages 319-356, June.
    9. Felipe Caro & Aparupa Das Gupta, 2022. "Robust control of the multi-armed bandit problem," Annals of Operations Research, Springer, vol. 317(2), pages 461-480, October.
    10. Kartikeya Puranam & Michael Katehakis, 2014. "On optimal bidding and inventory control in sequential procurement auctions: the multi period case," Annals of Operations Research, Springer, vol. 217(1), pages 447-462, June.
    11. Savas Dayanik & Semih O Sezer, 2023. "Model Misspecification in Discrete Time Bayesian Online Change Detection," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-27, March.
    12. Inchi Hu & Chi-Wen Jevons Lee, 2003. "Bayesian Adaptive Stochastic Process Termination," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 361-381, May.
    13. Agbo, Maxime, 2015. "A perpetual search for talents across overlapping generations: A learning process," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 131-145.
    14. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2021. "Managing mobile production-inventory systems influenced by a modulation process," Annals of Operations Research, Springer, vol. 304(1), pages 299-330, September.
    15. Jue Wang & Chi-Guhn Lee, 2015. "Multistate Bayesian Control Chart Over a Finite Horizon," Operations Research, INFORMS, vol. 63(4), pages 949-964, August.
    16. Apostolos Burnetas, 2022. "Learning and data-driven optimization in queues with strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 517-519, April.
    17. He Huang & DaPeng Liang & Liang Liang & Zhen Tong, 2019. "Research on China’s Power Sustainable Transition Under Progressively Levelized Power Generation Cost Based on a Dynamic Integrated Generation–Transmission Planning Model," Sustainability, MDPI, vol. 11(8), pages 1-21, April.
    18. Ronald Ortner, 2013. "Adaptive aggregation for reinforcement learning in average reward Markov decision processes," Annals of Operations Research, Springer, vol. 208(1), pages 321-336, September.

    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:annopr:v:208:y:2013:i:1:d:10.1007_s10479-012-1121-6. 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.