Date/heure
24 avril 2025
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Ed Cohen (Imperial College, London)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
Statistical methodology for spatial point patterns has traditionally focused on Euclidean data and planar surfaces. However, with recent advances in 3D biological imaging technologies targeting protein molecules on a cell’s plasma membrane, spatial point patterns are now being observed on complex shapes and manifolds whose geometry must be respected for principled inference. Consequently, there is now a demand for tools that can analyse these data for important scientific studies in cellular and micro-biology. Motivated by studying the spatial distribution of LPS proteins on the surface of E-Coli, we develop the fundamental functional summary statistics for the analysis of point patterns to general convex bounded shapes and demonstrate how they can be used to test for complete spatial randomness. We then develop their multi-type extensions, together with a test for independence of the component marginal processes. To support these methods, we introduce a plug-in estimator for the intensity of a spatial point process on a manifold. We conclude with a discussion on how these methods can readily be extended to a class of non-convex shapes. This talk will aim to provide an accessible overview of the references below.
References:
Ward, E.A.K. Cohen, N. M. Adams. Testing for complete spatial randomness on 3-dimensional bounded convex shapes. Spatial Statistics, Vol. 41, 2021.
Ward, H. S. Battey and E. A. K. Cohen. Nonparametric estimation of the intensity function of a spatial point process on a Riemannian manifold. Biometrika, Vol. 110, 2023.
Kumar, P. Inns, S. Ward, V. Lagage, J. Wang, R. Kaminska, S. Uphoff, E. A. K. Cohen, G. Mamou and C. Kleanthous. Immobile lipopolysaccharides and outer membrane proteins differentially segregate in growing Escherichia coli. Proceedings of the National Academy of Sciences, 122 (10), 2025
Ward, E. A. K. Cohen and N. M. Adams. Functional summary statistics and testing for independence in marked point patterns on the surface of three-dimensional convex shapes. Spatial Statistics, Vol. 67, 2025