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The semi-Markov beta-Stacy process: a Bayesian non-parametric prior for semi-Markov processes

Author

Listed:
  • Andrea Arfè

    (Harvard Medical School)

  • Stefano Peluso

    (University of Milano-Bicocca)

  • Pietro Muliere

    (Bocconi University)

Abstract

The literature on Bayesian methods for the analysis of discrete-time semi-Markov processes is sparse. In this paper, we introduce the semi-Markov beta-Stacy process, a stochastic process useful for the Bayesian non-parametric analysis of semi-Markov processes. The semi-Markov beta-Stacy process is conjugate with respect to data generated by a semi-Markov process, a property which makes it easy to obtain probabilistic forecasts. Its predictive distributions are characterized by a reinforced random walk on a system of urns.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:1:d:10.1007_s11203-020-09224-2
    DOI: 10.1007/s11203-020-09224-2
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    References listed on IDEAS

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    1. 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.
    2. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    3. Glen A. Satten & Maya R. Sternberg, 1999. "Fitting Semi-Markov Models to Interval-Censored Data with Unknown Initiation Times," Biometrics, The International Biometric Society, vol. 55(2), pages 507-513, June.
    4. Bulla, Jan, 2006. "Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series," MPRA Paper 7675, University Library of Munich, Germany.
    5. 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.
    6. 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.
    7. Giovanni Masala, 2013. "Hurricane Lifespan Modeling through a Semi‐Markov Parametric Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(4), pages 369-384, July.
    8. 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.
    9. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.
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