### Nonparametric Bayesian analysis for assessing homogeneity in k × l contingency tables with fixed right margin totals

### Abstract

"In this work I postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. I assume that cell count vectors for each group are conditionally independent, with multinomial distribution given vectors of classification probabilities. In turn, these vectors of probabilities are assumed to be a sample from a distribution F, and the prior distribution of F is assumed to be a Dirichlet process, centered on a probability measure ? and with weight c. I also assume a prior distribution for c, as a way of obtaining a better control on the clustering structure induced by the Dirichlet process. I use this setting to assess homogeneity of classification probabilities, and propose a ""Bayes factor."" I derive exact expressions for the relevant quantities. These can be directly computed when the number of rows k is small, and through the sequential importance sampling algorithm proposed by MacEachern, Clyde, and Liu when k is moderate or large. The methods are illustrated with several examples."

### Más información

Título de la Revista: | Journal Of The American Statistical Association |

Volumen: | 93 |

Número: | 443 |

Editorial: | AMER STATISTICAL ASSOC |

Fecha de publicación: | 1998 |

Página de inicio: | 1140 |

Página final: | 1149 |

URL: | http://www.scopus.com/inward/record.url?eid=2-s2.0-0032328001&partnerID=q2rCbXpz |

DOI: |
10.1080/01621459.1998.10473775 |