Implicative Analysis for Multivariate Binary Data using an Imprecise Dirichlet Model

Bayesian implicative analysis was proposed for summarizing the association in a 22 contingency table in terms possibly asymmetrical such as, e.g., presence of feature a implies, in general, presence of feature b" a quasi-implies b" in short. Here, we consider the multivariate version of this problem: having n units which are classi ed according to q binary questions, we want to summarize the association between questions in terms of quasi-implications between features. We will rst show how at a descriptive level the notion of implication can be weakened into that of quasiimplication. The inductive step assumes that the n units are a sample from a 2q-multinomial population. Uncertainty about the patterns' true frequencies is expressed by an imprecise Dirichlet model which yields upper and lower posterior probabilities for any quasiimplicative statement. This model is shown to have several advantages over the Bayesian models based on a single Dirichlet prior, especially w...

• Type: Conference
• Year: 1999
• Where: ISIPTA
• Authors: Jean-Marc Bernard
• Keywords: Bayesian Implicative Analysis, Imprecise Dirichlet Model, ISIPTA 1999, Lower Posterior Probabilities, Mathematics