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Hypotheses testing and posterior concentration rates for semi-Markov processes

Author

Listed:
  • I. Votsi

    (Institut du Risque et de l’Assurance, Le Mans Université)

  • G. Gayraud

    (Université de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne))

  • V. S. Barbu

    (Université de Rouen-Normandie, UMR 6085)

  • N. Limnios

    (Université de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne))

Abstract

In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous-time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and countable state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09247-3
    DOI: 10.1007/s11203-021-09247-3
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    References listed on IDEAS

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    Cited by:

    1. Vlad Stefan Barbu & Guglielmo D’Amico & Andreas Makrides, 2022. "A Continuous-Time Semi-Markov System Governed by Stepwise Transitions," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    2. Vlad Stefan Barbu & Guglielmo D’Amico & Thomas Gkelsinis, 2021. "Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.

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