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Article Dans Une Revue Stochastic Processes and their Applications Année : 2020

Posterior consistency for partially observed Markov models

Résumé

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.

Dates et versions

hal-04081621 , version 1 (25-04-2023)

Identifiants

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Randal Douc, Jimmy Olsson, François Roueff. Posterior consistency for partially observed Markov models. Stochastic Processes and their Applications, 2020, 130 (2), pp.733-759. ⟨10.1016/j.spa.2019.03.012⟩. ⟨hal-04081621⟩
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