Roughly speaking, an ALF metric of real dimension 4n should be a metric such that its asymptotic cone is 4n - 1 dimensional, the volume growth of this metric is of order 4n - 1 and its sectional curvature tends to 0 at infinity. We will show that the Taub-NUT deformation of a hyperkahler cone with respect to a locally free circle action is ALF hyperkahler. Modelled on this metric at infinity, we can show the existence of ALF Calabi-Yau metric on certain crepant resolutions. In particular, there exist ALF Calabi-Yau metrics on canonical bundles of classical homogeneous Fano contact manifolds.

Classical inference methods fail when applied to data-driven test hypotheses. Selective inference is particularly relevant post-clustering, typically when testing a difference in the mean between two clusters. Thus, dedicated methodologies are required to obtain statistical quarantees for these selective inference problems. In this work, we address convex clustering with l1 penalization, by leveraging related selective inference tools for regression, based on Gaussian vectors conditioned to polyhedral sets.

In the one-dimensional case, we prove a polyhedral characterization of obtaining given clusters, then enables us to suggest a test procedure with statistical guarantees. This characterization also allows us to provide a computationally efficient regularization path algorithm. Then, we extend the above test procedure and guarantees to some multi-dimensional clusterings. Our methods are implemented in the R package poclin.

Le développement de système de suivi GPS léger et très autonome permet de suivre les déplacements des individus de manière précise précise et peu invasive. Ces données de trajectoires sont comprises par les écologues comme le reflet des besoins internes de l'animal, envisagé comme un problème de segmentation, et de sa réponse à l'environnement. Dans cet exposé, je présenterai plusieurs développement statistiques récents, reposant sur des approches à variables latentes, qui visent à extraire ce type d'information des données déplacement. Ces méthodes posent des questions intéressantes en terme de modélisation, d'inférence et de choix de modèles qui seront détaillées dans l'exposé.

Reférences :

Gloaguen, Pierre, Marie-Pierre Etienne, and Sylvain Le Corff. "Stochastic differential equation based on a multimodal potential to model movement data in ecology." Journal of the Royal Statistical Society Series C: Applied Statistics 67.3 (2018): 599-619. Patin, Rémi, et al. "Identifying stationary phases in multivariate time series for highlighting behavioural modes and home range settlements." Journal of Animal Ecology 89.1 (2020): 44-56.