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Identifiability conditions for partially-observed Markov chains

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Advanced Monte Carlo Methods for Complex Inference Problems

Co-authors: Franois ROUEFF (LTCI, UMR 5141 , Telecom Paristech, France), Tepmony SIM (LTCI, UMR 5141 , Telecom Paristech, France)

This paper deals with a parametrized family of partially-observed bivariate Markov chains. We establish that the limit of the normalized log-likelihood is maximized when the parameter belongs to the equivalence class of the true parameter, which is a key feature for obtaining consistency of the Maximum Likelihood Estimators in well-specified models. A novel aspect of this work is that geometric ergodicity of the Markov chain associated to the complete data, or exponential separation on measures are no more needed provided that the invariant distribution is assumed to be unique, regardless its rate of convergence to the equilibrium. The result is presented in a general framework including both fully dominated or partially dominated models as Hidden Markov models or Observation-Driven times series of counts.

This talk is part of the Isaac Newton Institute Seminar Series series.

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