Rencontres Statistiques Lyonnaises

Continuous testing for Poisson process intensities : A new perspective on scanning statistics

par Franck Picard (LBBE)

Fokko du Cloux (Braconnier)

Fokko du Cloux


Première partie : exposé préliminaire sur l'analyse de données en génomique Seconde partie : We propose a novel continuous testing framework to test the intensities of Poisson Processes. This framework allows a rigorous definition of the complete testing procedure, from an infinite number of hypothesis to joint error rates. Our work extends traditional procedures based on scanning windows, by controlling the family-wise error rate and the false discovery rate in a non-asymptotic manner and in a continuous way. The decision rule is based on a pvalue process that can be estimated by a Monte-Carlo procedure. We also propose new test statistics based on kernels. Our method is applied in Neurosciences and Genomics through the standard test of homogeneity, and the two-sample test.
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