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

Abstract

We propose a continuous testing framework to test the intensities of Poisson processes that allows a rigorous definition of the complete testing procedure, from an infinite number of hypotheses to joint error rates. Our work extends procedures based on scanning windows by controlling the familywise error rate and the false discovery rate in a non-asymptotic manner and in a continuous way.We introduce the p-value process on which the decision rule is based. Our method is applied in neuroscience via the standard homogeneity and two-sample tests.