Premium
Functionally Compatible Local Characteristics for the Local Specification of Priors in Graphical Models
Author(s) -
ASCI CLAUDIO,
PICCIONI MAURO
Publication year - 2007
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00551.x
Subject(s) - mathematics , conjugate prior , wishart distribution , prior probability , inverse wishart distribution , exponential family , graphical model , poisson distribution , gamma distribution , multivariate normal distribution , graph , joint probability distribution , multivariate statistics , marginal distribution , gaussian , exponential function , statistics , combinatorics , bayesian probability , random variable , mathematical analysis , physics , quantum mechanics
. The local specification of priors in non‐decomposable graphical models does not necessarily yield a proper joint prior for all the parameters of the model. Using results concerning general exponential families with cuts, we derive specific results for the multivariate Gamma distribution (conjugate prior for Poisson counts) and the Wishart distribution (conjugate prior for Gaussian models). These results link the existence of a locally specified joint prior to the solvability of a related marginal problem over the cliques of the graph.