L'analyse implicative bayésienne multivariée d'un questionnaire binaire : quasi-implications et treillis de Galois simplifié

Mathématiques et sciences humaines. Mathematics and social sciences

Bernard, Jean-Marc¹  Poitrenaud, Sébastien¹ 

关键词: binary data;    boolean methods;    multivariate implicative index;    bayesian inference;    imprecise probabilities;    imprecise dirichlet model;   

DOI  :  10.4000/msh.2794

学科分类：数学（综合）

来源: College de France * Ecole des Hautes Etudes en Sciences Sociales (E H E S S)

【 摘 要 】

We propose a new method for simplifying the Galois lattice associated to a binary questionnaire (n units classified according to q binary questions). The method consists in weakening the implications borne by the lattice into quasi-implications. At the descriptive level, the method involves a new measure for quasi-implications (the "multivariate implicative index") which satisfies some requirements of invariance by logical equivalence. At the inductive level, uncertainty about the patterns' true frequencies is expressed by an imprecise-Dirichlet model. This model is shown to have several advantages over the usual non-informative Bayesian approach based on a single Dirichlet prior, especially for the case where n is small in comparison to 2q. An important feature of the method is that it provides two implicative summaries, descriptive and inductive, which both constitute simplified versions of the initial Galois lattice.

【 授权许可】

Unknown