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Parametrizations and reference priors for multinomial decomposable graphical models

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  • Consonni, Guido
  • Massam, Hélène

Abstract

Given a multinomial decomposable graphical model, we identify several alternative parametrizations; in particular we consider conditional probabilities of clique-residuals given separators, as well as generalized log-odds-ratios. For each such parametrization, we construct the corresponding reference prior for suitable groupings of the parameters. Each one of the reference priors we obtain is conjugate to the likelihood and is proper. Furthermore, all these priors are equivalent, in the sense that they can be deduced from each other by a change of variable. We also derive estimators of cell-probabilities based on the reference prior. Finally, we discuss in detail a parametrization associated to a collection of variables representing a cut for the statistical model, and derive the corresponding reference prior.

Suggested Citation

  • Consonni, Guido & Massam, Hélène, 2012. "Parametrizations and reference priors for multinomial decomposable graphical models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 380-396.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:380-396
    DOI: 10.1016/j.jmva.2011.08.001
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    References listed on IDEAS

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    1. Petros Dellaportas & Claudia Tarantola, 2005. "Model determination for categorical data with factor level merging," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 269-283, April.
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    3. Guido Consonni & Piero Veronese, 2001. "Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 377-406, June.
    4. Hara, Hisayuki & Takemura, Akimichi, 2007. "Improving on the maximum likelihood estimators of the means in Poisson decomposable graphical models," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 410-434, February.
    5. Y. Yang, 1995. "Invariance of the reference prior under reparametrization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 83-94, June.
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