Combinatorial Inference In Geometric Data Analysis
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Combinatorial Inference in Geometric Data Analysis
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. Features: 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.
Geometric Data Analysis
Author: Brigitte Le Roux
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-01-16
Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzécri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. Chapter 9, Research Case Studies, is nearly a book in itself; it presents the methodology in action on three extensive applications, one for medicine, one from political science, and one from education (data borrowed from the Stanford computer-based Educational Program for Gifted Youth ). Thus the readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis.
Multivariate scaling methods and the reconstruction of social spaces
Author: Alice Barth
language: en
Publisher: Verlag Barbara Budrich
Release Date: 2023-10-02
Der Sammelband vereint Beiträge von führenden Forscherinnen und Forschern im Bereich statistischer Methoden und deren Anwendung in den Sozialwissenschaften mit einem besonderen Fokus auf sozialen Räumen. Multivariate Skalierungsmethoden für kategoriale Daten, speziell Korrespondenzanalyse, werden verwendet um die wichtigsten Dimensionen aus komplexen Kreuztabellen mit vielen Variablen zu extrahieren und Zusammenhänge in den Daten bildlich darzustellen. In diesem Band werden statistische Weiterentwicklungen, grundsätzliche methodologische Überlegungen und empirische Anwendungen multivariater Analysemethoden diskutiert. Mehrere Anwendungsbeispiele thematisieren verschiedene Aspekte des Raumes und deren soziologische Bedeutung: die Rekonstruktion „sozialer Räume“ mit statistischen Methoden, die Illustration räumlicher Beziehungen zwischen Nähe, Distanz und Ungleichheit, aber auch konkrete Interaktionen in urbanen Räumen. Der Band erscheint zur Würdigung der wissenschaftlichen Leistungen von Prof. Jörg Blasius.