Journées de statistique - Tests multiples

Lundi et Mardi 24-25/09/2018.

Description

Ces journées ont pour but de réunir des chercheurs en statistique et analyse de données, notamment autour de la problématique des tests multiples.

Elles incluent la soutenance de thèse de Marine Roux, intitulée Graph Inference by Multiple Testing with Application to Neuroimaging

Orateurs

Raphaël Bacher, Data Grenoble Institute.

Jean-Michel Becu, ACOEM.

Pierre Neuvial, Institut de Mathématiques de Toulouse, <site>

Patricia Reynaud-Bouret, Université de Nice Sophia Antipolis, <site>

Etienne Roquain, Université Sorbonne, <site>

Programme prévisionnel

Lundi 11h00 - 12h00	Etienne Roquain (Université Sorbonne)
	Post hoc false positive control - part 1: general framework
	We present new confidence bounds on the false positives contained in subsets S of selected null hypotheses. The coverage probability holds simultaneously over all subsets S, which means that the obtained confidence bounds are "post hoc". Therefore, S can be chosen arbitrarily, possibly by using the data set several times. This property is particularly important in practice to make a rigorous selective inference and ensure reproducibility of the results. This part will focus on bounds that can be derived by classical inequalities (Simes or DKW). Further extensions will be discussed by Pierre Neuvial in part 2.
	This is a joint work with Gilles Blanchard, Guillermo Durand and Pierre Neuvial.
	salle 106
Lundi 14h00 - .	Soutenance de thèse de Marine Roux (GIPSA-lab, Grenoble)
	Graph Inference by Multiple Testing with Application to Neuroimaging
	This thesis is motivated by the analysis of the functional magnetic resonance imaging (fMRI). The need for methods to build such structures from fMRI data gives rise to exciting new challenges for mathematics. In this regards, the brain connectivity networks are modelized by a graph and we study some procedures that allow us to infer this graph. More precisely, we investigate the problem of the inference of the structure of an undirected graphical model by a multiple testing procedure. The structure induced by both the correlation and the partial correlation are considered. The statistical tests based on the latter are known to be highly dependent and we assume that they have an asymptotic Gaussian distribution. Within this framework, we study some multiple testing procedures that allow a control of false edges included in the inferred graph. First, we theoretically examine the False Discovery Rate (FDR) control of Benjamini and Hochberg's procedure in Gaussian setting for non necessary positive dependent statistical tests. Then, we explore both the FDR and the Family Wise Error Rate (FWER) control in asymptotic Gaussian setting. We present some multiple testing procedures, well-suited for correlation (resp. partial correlation) tests, which provide an asymptotic control of the FWER. Furthermore, some first theoretical results regarding asymptotic FDR control are established. Second, the properties of the multiple testing procedures that asymptotically control the FWER are illustrated on a simulation study, for statistical tests based on correlation. We finally conclude with the extraction of cerebral connectivity networks on real data set.
	salle 1 - rdc
Mardi 10h00 - 11h00	Pierre Neuvial (Université de Toulouse)
	Post hoc false positive control - part 2: calibration and applications
	This talk is based on the post hoc framework introduced by Etienne Roquain in this own talk. I will explain how sharper post hoc false positive control may be obtained when the joint distribution of the test statistics under the null hypothesis is known, or satisfies a specific randomization assumption. These results will be illustrated by numerical experiments, and applied to the analysis of a gene expression data set.
	This is joint work with Gilles Blanchard, Guillermo Durand, Etienne Roquain and Benjamin Sadacca.
	salle 106
Mardi 11h00 - 12h00	Jean-Michel Becu (ACOEM)
	salle 106
Mardi 12h00 - 14h00	Pause. Buffet froid.
	salle de convivialité - rdc
Mardi 14h00 - 15h00	Patricia Reynaud-Bouret (Université de Nice Sophia Antipolis)
	Continuous testing for Poisson process intensities: A new perspective on scanning statistics
	This is a joint work with F. Picard (LBBE, Lyon) and E. Roquain (Paris 6). 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 hypothesis to joint error rates. Our work extends 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. We introduce the p-value process on which the decision rule is based. Our method is applied in neuroscience on spike trains via the standard homogeneity and two-sample tests.
	salle 106
Mardi 15h00 - 16h00	Raphaël Bacher (Data Grenoble Institute)
	The COMET method : detecting extragalactic structures while ensuring global error control.
	In this talk we present a new detection procedure of spatially extended target in images, with a global error control of the False Discovery Rate (FDR). The novelty of this approach consists in taking into account the spatial structures of the target into the FDR control procedure. A generic framework is discussed and a method based on this framework is implemented. Results on simulated data show conclusive gains in detection power for a nominal control level. The method is also applied to the detection of extragalactic structures on real data produced by the astronomical instrument MUSE.
	salle 106

Inscription

Les exposés sont ouverts à tous, sans frais d'inscription.

Merci de nous contacter par mail pour vous inscrire : irene.gannaz at insa-lyon.fr. L'inscription est nécessaire afin que nous puissions prévenir le bâtiment IMAG (accès badgé à la salle 106).

Le repas du mardi midi est inclus dans les journées.

Attention, seul le repas du mardi midi est prévu dans le workshop.

Lieu

Les exposés auront lieu au bâtiment IMAG, sur le Campus de St Martin d'Hères, Grenoble.

Attention : un badge étant nécessaire pour accéder à certaines salles, il est préférable de nous contacter pour prévenir de votre venue.

Si vous ne disposez pas du badge, présentez vous à l'accueil du bâtiment IMAG.

Le plan pour venir est disponible ici : Plan du campus, et des informations peuvent être trouvées ici : Adresses et accès.

Par tramway, depuis Grenoble centre et gares, prendre la Ligne B Direction : « Gières Plaine des Sports », arrêt « Gabriel Fauré ».

Organisateurs	Sophie Achard	GIPSA-lab	Grenoble
	Jean-Baptiste Aubin	ICJ	Lyon
	Vincent Brault	LJK	Grenoble
	Jean-Baptiste Durand	LJK	Grenoble
	Irène Gannaz	ICJ	Lyon
	Samuela Leoni-Aubin	ICJ	Lyon

Contact : irene.gannaz at insa-lyon.fr

Financement

Cette journée est organisée dans le cadre d'un projet financé par la FRMRAA.