Random permutations have had a long history in statistic tests since Fisher, a century ago, investigated on whether a Lady could or could not determine which of the milk or the tea was first poured into the cup. The method of random permutations he developed yielded modern bootstrap approaches. Those now apply to more and more complex data, particularly in neurosciences in the context of synchronisation detection. The synchronisation phenomena between neurons are widely considered as elements of the neural code, which would explain how the information from outside is encoded in neural activity. The works of the physicist S. Grün at the end of the 90s turned synchronisations analysis into a problem of multiple tests of independence on spikes' trains, which report on the registrered neural activity and, from a mathematical point of view, can be modelled by point processes. In several recent papers, Mélisande Albert (IMT), Yann Bouret (LPMC), Magalie Fromont (IRMAR) and Patricia Reynaud-Bouret (LJAD) brought a mathematical proof of the convergence of the bootstrap distribution for very general variables of point process' type. They analyse the properties of the surrogate data methods used in neurosciences and based on bootstrap. Finally, they prove that the test of independence by permutation is the most reliable one among all tests.
Read the full article on the Insmi French website.
 M. Albert, Y. Bouret, M. Fromont, P. Reynaud-Bouret. Bootstrap and permutation tests of independence for point processes, Annals of Statistics, 43(6), 2537-2564 (2015).
 M. Albert, Y. Bouret, M. Fromont, P. Reynaud-Bouret. Surrogate data methods based on a shuffling of the trials for synchrony detection : the centering issue, to be published in Neural Computation (2016).
Mélisande Albert | Institut de mathématiques de Toulouse | UMR 5219 | CNRS, INSA Toulouse, Univ. Toulouse Capitole, Univ. Toulouse Jean Jaurès, Univ. Toulouse Paul Sabatier
Yann Bouret | Laboratoire Physique de la Matière Condensée | UMR 7336 | CNRS, Université de Nice-Sophia Antipolis
Magalie Fromont | Institut de recherche mathématique de Rennes | UMR 6625 | CNRS, ENS Rennes, INSA Rennes, Univ. Haute Bretagne, Univ. Rennes 1
Patricia Reynaud-Bouret | Laboratoire J. A. Dieudonné | UMR 7351 | CNRS, Univ. Nice Sophia Antipolis