Algebraic Bayesian analysis of contingency tables with possibly zero-probability cells.

Guido Consonni, Giovanni Pistone

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5 Citazioni (Scopus)

Abstract

In this paper we consider a Bayesian analysis of contingency tables allowing for the possibility that cells may have probability zero. In this sense we depart from standard log-linear modeling that implicitly assumes a positivity constraint. Our approach leads us to consider mixture models for contingency tables, where the components of the mixture, which we call model-instances, have distinct support. We rely on ideas from polynomial algebra in order to identify the various model instances. We also provide a method to assign prior probabilities to each instance of the model, and we describe methods for constructing priors on the parameter space of each instance. We illustrate our methodology through a 5 × 2 table involving two structural zeros, as well as a zero count. The results we obtain show that our analysis may lead to conclusions that are substantively different from those that would obtain in a standard framework, wherein the possibility of zero-probability cells is not explicitly accounted for.
Lingua originaleEnglish
pagine (da-a)1355-1370
Numero di pagine16
RivistaStatistica Sinica
Volume17
Stato di pubblicazionePubblicato - 2007

Keywords

  • Algebraic statistics
  • Log-linear model

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