IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v88y2000i1p59-78.html
   My bibliography  Save this article

Urn schemes and reinforced random walks

Author

Listed:
  • Muliere, P.
  • Secchi, P.
  • Walker, S. G.

Abstract

We define a reinforced urn process (RUP) to be a reinforced random walk on a state space of urns and we show its partial exchangeability. When it is recurrent, a RUP is a mixture of Markov chains and we characterize its mixing distribution on the space of stochastic matrices. Many Bayesian nonparametric priors, like Pólya trees, the beta-Stacy process and, in general, neutral to the right processes can be derived from RUPs. Applications to survival data are examined.

Suggested Citation

  • Muliere, P. & Secchi, P. & Walker, S. G., 2000. "Urn schemes and reinforced random walks," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 59-78, July.
    • Handle: RePEc:eee:spapps:v:88:y:2000:i:1:p:59-78
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00119-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Cheng, Dan & Cirillo, Pasquale, 2018. "A reinforced urn process modeling of recovery rates and recovery times," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 1-17.
    2. Muliere, Pietro & Secchi, Piercesare & G. Walker, Stephen, 2003. "Reinforced random processes in continuous time," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 117-130, March.
    3. Muliere, Pietro & Secchi, Piercesare & Walker, Stephen, 2005. "Partially exchangeable processes indexed by the vertices of a k-tree constructed via reinforcement," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 661-677, April.
    4. Pasquale Cirillo & Jürg Hüsler & Pietro Muliere, 2013. "Alarm Systems and Catastrophes from a Diverse Point of View," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 821-839, December.
    5. Dan Cheng & Pasquale Cirillo, 2019. "An Urn-Based Nonparametric Modeling of the Dependence between PD and LGD with an Application to Mortgages," Risks, MDPI, vol. 7(3), pages 1-21, July.
    6. Souto Arias, Luis A. & Cirillo, Pasquale, 2021. "Joint and survivor annuity valuation with a bivariate reinforced urn process," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 174-189.
    7. John J. McCall, 2004. "Induction: From Kolmogorov and Solomonoff to De Finetti and Back to Kolmogorov," Metroeconomica, Wiley Blackwell, vol. 55(2‐3), pages 195-218, May.
    8. Mezzetti, Maura & Muliere, Pietro & Bulla, Paolo, 2007. "An application of reinforced urn processes to determining maximum tolerated dose," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 740-747, April.
    9. Fortini, S. & Petrone, S., 2012. "Hierarchical reinforced urn processes," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1521-1529.
    10. Lorenzo Trippa & Paolo Bulla & Sonia Petrone, 2011. "Extended Bernstein prior via reinforced urn processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 481-496, June.
    11. Stefano Peluso & Antonietta Mira & Pietro Muliere & Alessandro Lomi, 2016. "International Trade: a Reinforced Urn Network Model," Papers 1601.03067, arXiv.org.
    12. Pasquale Cirillo & Pietro Muliere, 2013. "An urn-based Bayesian block bootstrap," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 93-106, January.
    13. Paolo Bulla & Pietro Muliere, 2007. "Bayesian Nonparametric Estimation for Reinforced Markov Renewal Processes," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 283-303, October.
    14. Andrea Arfè & Stefano Peluso & Pietro Muliere, 2021. "The semi-Markov beta-Stacy process: a Bayesian non-parametric prior for semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 1-15, April.
    15. Paolo Leonetti, 2018. "Finite Partially Exchangeable Laws Are Signed Mixtures of Product Laws," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-214, August.
    16. Cirillo, Pasquale & Hüsler, Jürg, 2011. "Extreme shock models: An alternative perspective," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 25-30, January.
    17. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.

    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:eee:spapps:v:88:y:2000:i:1:p:59-78. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.