Parametrizations and reference priors for multinomial decomposable graphical models

Guido Consonni, Hélène Massam

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)380-396
Number of pages17
JournalJournal of Multivariate Analysis
Volume105
DOIs
Publication statusPublished - 2012

Keywords

  • Graphical model
  • Reference prior

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