Testing the spatial clustering with fast and robust analytical statistics
Résumé : In many scientific areas such as cellular biology, the analysis of objects’ spatial distribution can be used to infer their interactions and interplay with their environment. One crucial question is to know whether the observed objects organization is random or if key spatial features such as clusters can be characterized. A standard statistical tool is the the Ripley’s K function whose mean value under spatial randomness is known. However, measuring the significance of K function’s deviations from its reference level is very cumbersome and computationally heavy as it involves Monte-Carlo resampling and fitting. We propose here two major improvements which lead to a fast and robust analytical method. First, we estimate analytically the quantiles of the Ripley’s K function under spatial randomness by computing the skewness and the kurtosis of K in any field of view and by then using the Cornish-Fisher expansion of its critical quantiles. Second, we directly relate standard features such as clusters size to essential properties of the Ripley’s K function. We used our statistical framework to analyze the spatial organization of endocytic spots in clathrin-dependent and clathrin independent pathways. We found that clathrin spots are randomly distributed at cell membrane while clathrin-independent spots are organized in clusters with a radius of about 2 micrometers.
Cet exposé se tiendra en salle C20-13, 20ème étage, Université Paris 1, Centre Pierre Mendès-France, 90 rue de Tolbiac, 75013 Paris (métro : Olympiades).