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/ Département de mathématiques et de statistique

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Dubuc, Serge


Emeritus and Honorary professor

Faculty of Arts and Science - Department of Mathematics and Statistics



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Utilisation de splines monotones afin de condenser des tables de mortalité dans un contexte bayésien Theses and supervised dissertations / 2011-04
Patenaude, Valérie
This master’s thesis is about the estimation of bivariate tables which are monotone within the rows and/or the columns, with a special interest in the approximation of life tables. This problem is approached through a nonparametric Bayesian regression model, in particular linear combinations of regression splines. By condensing a life table, our goal is to reduce its storage space without losing the entries’ accuracy. We will also study the reconstruction time of the table with our estimators. The properties of the reference table, specifically its monotonicity, must be preserved in the estimation. We are working with a monotone spline basis since splines are flexible and their derivatives can easily be manipulated. Those properties enable the imposition of constraints of monotonicity on our model. A brief review on univariate approximations of monotone functions is then extended to bivariate estimations. We use hierarchical Bayesian modeling to include the constraints in the prior distributions. We then explain the Markov chain Monte Carlo algorithm to obtain a posterior estimator. Finally, we study the estimator’s behaviour by applying our model on the Standard Normal table and the Student’s t table. We estimate our data of interest, the life table, to establish the improvement in data accessibility.

Méthodes de volumes finis pour les systèmes d'équations hyperboliques : applications en aérodynamique et en magnétohydrodynamique Theses and supervised dissertations / 2005
Touma, Rony
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.