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Theses

Inférence statistique dans les modèles mixtes à dynamique Markovienne

Abstract : The first part of this thesis deals with maximum likelihood estimation in Markovian mixed-effects models. More precisely, we consider mixed-effects hidden Markov models and mixed-effects diffusion models. In Chapter 2, we combine the Baum-Welch algorithm and the SAEM algorithm to estimate the population parameters in mixed-effects hidden Markov models. We also propose some specific procedures to estimate the individual parameters and the sequences of hidden states. We study the properties of the proposed methodologies on simulated datasets and we present an application to real daily seizure count data. In Chapter 3, we first suggest mixed-effects diffusion models for population pharmacokinetics. We estimate the parameters of these models by combining the SAEM algorithm with the extended Kalman filter. Then, we study the asymptotic properties of the maximum likelihood estimate in some mixed-effects diffusion models continuously observed on a fixed time interval when the number of subjects tends to infinity. Chapter 4 is dedicated to variable selection in general mixed-effects models. We propose a BIC adapted to the asymptotic context where both of the number of subjects and the number of observations per subject tend to infinity. We illustrate this procedure with some simulations.
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Submitted on : Saturday, June 6, 2020 - 8:54:16 AM
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  • HAL Id : tel-02810777, version 1
  • PRODINRA : 395977

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Maud Delattre. Inférence statistique dans les modèles mixtes à dynamique Markovienne. Life Sciences [q-bio]. Université Paris Sud - Paris 11, 2012. English. ⟨tel-02810777⟩

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