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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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    5. 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.
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    8. 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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