Geometric Data Analysis designates the approach of Multivariate Statistics that conceptualizes the set of observations as a Euclidean cloud of points. Combinatorial Inference in Geometric Data Analysis gives an overview of multidimensional statistical inference methods applicable to clouds of points that make no assumption on the process of generating data or distributions, and that are not based on random modelling but on permutation procedures recasting in a combinatorial framework.
It focuses particularly on the comparison of a group of observations to a reference population (combinatorial test) or to a reference value of a location parameter (geometric test), and on problems of homogeneity, that is the comparison of several groups for two basic designs. These methods involve the use of combinatorial procedures to build a reference set in which we place the data. The chosen test statistics lead to original extensions, such as the geometric interpretation of the observed level, and the construction of a compatibility region.
- Defines precisely the object under study in the context of multidimensional procedures, that is clouds of points
- Presents combinatorial tests and related computations with R and Coheris SPAD software
- Includes four original case studies to illustrate application of the tests
- Includes necessary mathematical background to ensure it is self–contained
This book is suitable for researchers and students of multivariate statistics, as well as applied researchers of various scientific disciplines. It could be used for a specialized course taught at either master or PhD level.
Table of Contents
Cloud of Points in a Geometric Space
Combinatorial Typicality Test
Geometric Typicality Test
Homogeneity Permutation Tests
Research Case Studies
Brigitte Le Roux is associate researcher at Laboratoire de Mathématiques Appliquées (MAP5/CNRS) of the Paris Descartes university and at the political research center of Sciences-Po Paris (CEVIPOF/CNRS). She completed her doctoral dissertation in applied mathematics at the Faculté des Sciences de Paris in 1970 that was supervised by Jean-Paul Benzécri. She has contributed to numerous theoretical research works and full scale empirical studies involving Geometric Data Analysis. She has authored and co-authored nine books, especially on Geometric Data Analysis (2004, Kluwer Academic Publishers) and Multiple Correspondence Analysis (2010, QASS series of Sage publications, n° 163).
Solène Bienaise is data scientist at Coheris (company). She completed her doctoral dissertation in applied mathematics in 2013 at the Paris Dauphine University, under the direction of Pierre Cazes and Brigitte Le Roux.
Jean-Luc Durand is associate professor at the Psychology department and researcher at LEEC (Laboratoire d’Ethologie Expérimentale et Comparée) of Paris 13 University. He completed his doctoral dissertation in Psychology at Paris Descartes University in 1989, supervised by Henry Rouanet. He teaches statistical methodology in psychology and ethology.