Séminaire de Probabilités et Statistique :

Le 07 décembre 2015 à 15:00 - UM - Bât 09 - Salle de conférence (1er étage)

Présentée par Picard Franck - CNRS

Continuous Testing for Poisson process intensities

Joint work with Etienne Roquain (Paris 6) , Anne-Laure Fougères (Lyon 1), Patricia Reynaud-Bouret (Nice) Next Generation Sequencing technologies now allow the genome-wide mapping of binding events along genomes, like the binding of transcription factors for instance. More generally, the field of epigenetics is interested in the regulation of the genome by features that are spatially organized. One open question that remains is the comparison of spatially ordered features along the genome, between biological conditions. An example would be to compare the location of transcription factors between disease and healthy individuals. We propose here to model the spatial occurences of genomic features in each condition by a Poisson process with a heterogeneous intensity on [0,1], and we restate the problem as the comparison of Poisson process intensites in continuous time. Contrary to global testing approaches that consist in testing whether the two intensities are equal on [0,1], we focus on a local testing strategy using scanning windows. Our method is based on kernel to build the test statistics, and on monte-carlo simulations to compute the p-value process. By using the continuous testing framework, we provide a procedure that controls the Family Wise Error Rate as well as the False Discovery Rate in continous time. We illustrate our method on experimental data, and discuss its extensions in the general framework of testing for Poisson process intensities.