Combinatorial Inference in Geometric Data Analysis

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Combinatorial Inference in Geometric Data AnalysisIn this talk, we present statistical inference methods for Geometric Data Analysis (GDA) that are not based on random modeling, but on permutation procedures recast in a combinatorial framework. The combinatorial approach, which is entirely free from assumptions, is the most in harmony with inductive data analysis. The methods are applicable to any IndividualsXvariables table, with structuring factors on individuals (i.e. external categorical variables not used for construction the clouds), and either numerical (PCA) or categorized (MCA) variables. In GDA the usual sampling models, with their drastic assumptions, are simply not appropriate. We first introduce the test of comparison of the mean of a subcloud to a point a reference. Then we develop procedures dealing with the typicality of a subcloud of individuals with a generalization of test-values. Lastly, we present homogeneity tests for comparing several subclouds. In each case, we define the p-value and a compatibility (confidence) zone.References:Bienaise S.(2013). Méthodes d'inférence combinatoire sur un nuage euclidien/Etude statistique de la cohorte EPIEG, PhD Université Paris Dauphine.Edgington E., & Onghena P. (2007). Randomization tests. CRC Press.Pesarin F. (2001). Multivariate permutation tests: with applications in biostatistics (Vol. 240). Chichester: Wiley.Le Roux B., Rouanet H. (2004). Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis}, Dordrecht: Kluwer.Rouanet H., Bernard J-M., Lecoutre B. (1986). Nonprobabilistic statistical inference: A set-theoretic approach, The American Statistician, 49, 60-65.Rouanet, H., Bernard, J. M., Bert, M. C., Lecoutre, B., Lecoutre, M. P., & Le Roux, B. (1998). New ways in statistical methodology. From Significance Tests to Bayesian Inference. Berne: Peter Lang.