Séance du 30 novembre 2009

Lundi 30 novembre 2009

Organisateurs: Gersende Fort et Judith Rousseau

14h00 Andrew Gelman (Dept of Statistics and Dept of Political Science, Columbia University, New York)

Parameterization and Bayesian Modeling

Abstract: Progress in statistical computation often leads to advances in statistical modeling. For example, it is surprisingly common that an existing model is reparameterized, solely for computational purposes, but then this new configuration motivates a new family of models that is useful in applied statistics. One reason why this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood. In a Bayesian framework, however, a transformation of parameters typically suggests a new family of prior distributions. We discuss examples in censored and truncated data, mixture modeling, multivariate imputation, stochastic processes, and multilevel models.

15h00 Adeline Samson (IUT Paris Descartes, Laboratoire MAP5)

Parameter estimation for a bidimensional partially observed Ornstein-Uhlenbeck process with biological application.

Abstract: We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularisation in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE).Our aim is the estimation of the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to compute the exact likelihood using the Kalman filter recursion. We also propose a recursive computation of the gradient and hessian of the log-likelihood based on Kalman filtering, which allows to implement an easy numerical maximisation of the likelihood and the exact maximum likelihood estimator (MLE). Furthermore, we establish the link between the observations and an ARMA process and we deduce the asymptotic properties of the MLE.

16h00 Randal Douc (TELECOM SudParis)

Consistency of the maximum likelihood estimator in general hidden Markov models / Consistance de l'estimateur de maximum de vraisemblance pour des chaines de Markov cachées.

Résumé: Nous établissons dans ce travail la propriété de consistance du maximum de vraisemblance pour des modèles de chaines de Markov cachées où l'espace des états cachées est possiblement non compact. Sous une condition d'ergodicité géométrique de la chaine cachée, il est montré que la fonction de contraste asymptotique sépare la vraie valeur des autres valeurs du paramètre. Ce résultat, valide pour des mesures initiales positives possiblement non finies, permet ensuite de prouver la consistance suivant une technique ne faisant intervenir, ni l'oubli de la distribution initiale pour le filtre, ni la convergence de la log-vraisemblance normalisée pour d'autres valeurs du parametre.