Séance du 18 septembre 2017

Séance organisée par Thanh Mai Pham Ngoc et Judith Rousseau.

Lieu : IHP, Amphi Hermite

14.00 : Yohann de Castro (Université Paris-Sud)

Titre : Tests exacts de la moyenne d’un processus gaussien

Résumé : Dans cet exposé, on s'intéresse à construire et comparer des statistiques de tests exacts sur la moyenne d'un processus gaussien. On étudie trois tests : un test basé sur l'observation du processus sur une grille, le test obtenu en faisant tendre le pas de la grille vers zéro, et un test basé sur toute la trajectoire du processus. Référence :

Testing Gaussian Process with Applications to Super-Resolution (avec J.-M. Azaïs & S. Mourareau), arXiv 1706.00679 .

15.00 : James Watson (University of Oxford)

Titre : Modelling red blood cell production and drug induced red blood cell destruction in order to optimise a radical curative regimen for vivax malaria

Résumé : Primaquine is the only drug available to prevent relapse in vivax malaria. The main adverse effect of primaquine is potentially life-threatening anaemia due to the destruction of older red blood cells in individuals with glucose-6-phosphate dehydrogenase deficiency (G6PDd). G6PDd is the most common enzyme deficiency of man. Proper testing for G6PDd is often unavailable and this limits the use of primaquine for radical cure. A compartmental model of the dynamics of red blood cell production and destruction was designed to characterise primaquine-induced haemolysis using a holistic Bayesian analysis of all published data. This model is used to predict a safer alternative to the current primaquine regimen recommended for G6PD deficient individuals. This model suggests that primaquine could be safely administered with an escalating dose regimen over 20 days. This hypothesis will be tested in an adaptive Phase 1 trial and some optimal trial design issues are discussed.

16.00 : Axel Munk (University of Goettingen)

Titre : Blind Source Separation

Résumé : We discuss a new methodology for statistical recovery of linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. This problems occurs in a variety of areas, ranging from telecommunications and electrophysiology to cancer genetics. We show that exact recovery within a small neighborhood of the mixture is possible when the sources take values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error we obtain uniform confidence sets and optimal rates (up to log-factors) for all quantities. SLAM is efficiently computed as a nonconvex optimization problem by a dynamic program tailored to the finite alphabet assumption. Its performance is investigated in a simulation study. Finally, it is applied to assign copy-number aberrations (CNAs) from genetic sequencing data to different tumor clones and to estimate their proportions. Our approach is then extended to combinatorial linear models with finite alphabets. Commonalities and differences to nonnegative matric factorization and sparse recovery in linear models are discussed. In summary, the assumption of a finite alphabet is fundamental for recovery in blind demixing problems which are in general not solvable.

This is joint work with Merle Behr (Göttingen) and Chris Holmes (Oxford).