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Posterior consistency for partially observed Markov models
Univ Paris Saclay, Telecom SudParis, CNRS, UMR 5157, 9 Rue Charles Fourier, F-91000 Evry, France..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0003-0772-846X
Univ Paris Saclay, Telecom ParisTech, LTCI, 46 Rue Barrault, F-75013 Paris, France..
2020 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 132, no 2, p. 733-759Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
ELSEVIER , 2020. Vol. 132, no 2, p. 733-759
National Category
Probability Theory and Statistics
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URN: urn:nbn:se:kth:diva-267740DOI: 10.1016/j.spa.2019.03.012ISI: 000509814500014Scopus ID: 2-s2.0-85064636272OAI: oai:DiVA.org:kth-267740DiVA, id: diva2:1394371
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QC 20200218

Available from: 2020-02-18 Created: 2020-02-18 Last updated: 2020-02-18Bibliographically approved

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