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Posterior consistency for partially observed Markov models

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  • Douc, Randal
  • Olsson, Jimmy
  • Roueff, François

Abstract

We establish the posterior consistency for parametric, partially observed, fully dominated Markov models. The prior is assumed to assign positive probability to all neighborhoods of the true parameter, for a distance induced by the expected Kullback–Leibler divergence between the parametric family members’ Markov transition densities. This assumption is easily checked in general. In addition, we show that the posterior consistency is implied by the consistency of the maximum likelihood estimator. The result is extended to possibly improper priors and non-stationary observations. Finally, we check our assumptions on a linear Gaussian model and a well-known stochastic volatility model.

Suggested Citation

  • Douc, Randal & Olsson, Jimmy & Roueff, François, 2020. "Posterior consistency for partially observed Markov models," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 733-759.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:733-759
    DOI: 10.1016/j.spa.2019.03.012
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
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    8. Douc, R. & Doukhan, P. & Moulines, E., 2013. "Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2620-2647.
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    Cited by:

    1. Yonekura, Shouto & Beskos, Alexandros & Singh, Sumeetpal S., 2021. "Asymptotic analysis of model selection criteria for general hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 164-191.

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