False discovery rate analysis of brain diffusion direction maps

Diffusion tensor imaging (DTI) is a novel modality of magnetic resonance imaging that allows noninvasive mapping of the brain's white matter. A particular map derived from DTI measurements is a map of water principal diffusion directions, which are proxies for neural fiber directions. We consider a study in which diffusion direction maps were acquired for two groups of subjects. The objective of the analysis is to find regions of the brain in which the corresponding diffusion directions differ between the groups. This is attained by first computing a test statistic for the difference in direction at every brain location using a Watson model for directional data. Interesting locations are subsequently selected with control of the false discovery rate. More accurate modeling of the null distribution is obtained using an empirical null density based on the empirical distribution of the test statistics across the brain. Further, substantial improvements in power are achieved by local spatial averaging of the test statistic map. Although the focus is on one particular study and imaging technology, the proposed inference methods can be applied to other large scale simultaneous hypothesis testing problems with a continuous underlying spatial structure.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS133 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Critical points of convex perturbations of quadratic functionals

AbstractA relationship between PS-condition and convexity for functionals exhibiting resonance type behavior at infinity is established. This leads to new existence and multiplicity results for critical points

Inference for eigenvalues and eigenvectors of Gaussian symmetric matrices

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, $3\times3$ and $2\times2$ symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.Comment: Published in at http://dx.doi.org/10.1214/08-AOS628 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inverse set estimation and inversion of simultaneous confidence intervals

The preimage or inverse image of a predefined subset of the range of a deterministic function, called inverse set for short, is the set in the domain whose image equals that predefined subset. To quantify the uncertainty in the estimation of such a set, we propose data-dependent inner and outer confidence sets that are sub- and super-sets of the true inverse set with a given confidence. Existing methods require strict assumptions, and the predefined subset of the range is usually an excursion set for only one single level. We show that by inverting pre-constructed simultaneous confidence intervals, commonly available for different kinds of data, multiple confidence sets of multiple levels can be simultaneously constructed with the desired confidence non-asymptotically. The method is illustrated on dense functional data to determine regions with rising temperatures in North America and on logistic regression data to assess the effect of statin and COVID-19 on clinical outcomes of in-patients

L’évolution des enfants difficiles

Dans cet article, les auteurs relatent une recherche faite, dans le cadre du projet Concordia Longitudinal Risk Project, sur l'ajustement des enfants socialement atypiques durant l'adolescence. Plus précisément, ils tentent de répondre à la question suivante: Quels comportements de l'enfant et quelles tangentes de son développement mènent à des problèmes psychologiques majeurs à l'adolescence et à l'âge adulte? Après une analyse complexe de divers facteurs, leurs résultats indiquent que les enfants perçus comme agressifs, repliés sur eux-mêmes ou souvent agressifs et repliés sur eux-mêmes par leur camarades, sont susceptibles d'avoir des problèmes à l'adolescence. Ils explicitent ensuite selon ces trois groupes les difficultés de chacun.In this article, the authors discuss a study carried out during a Concordia Longitudinal Risk Project that deals with the adjustment of socially atypical children in their adolescent years. More precisely, they try to answer the following question : What child behaviors and which tangents of their development lead to major psychological problems as an adolescent and as an adult? After a complex analysis of various factors, their results indicate that children perceived as aggressive, keeping to themselves or often aggressive and keeping to themselves because of peer pressure, are liable to have problems in their adolescent years. The authors then elaborate on the difficulties experienced by each of these three groups