A Characterization of the Dirichlet Distribution Through Global and Local Independence - Geiger, Dan; Heckerman, David (2003)
We provide a new characterization of the Dirichlet distribution. Let [[formula] be positive random variables that sum to unity. Define [formula]. We prove that if [formula] are mutually independent and [formula] are mutually independent (where [formula] are defined analogously), and assuming strictly positive pdfs, then the pdf of [formula] is Dirichlet. this characterization implies that under assumptions made by several previous authors for selecting a Bayesian-network structure out of a set of candidate structures, a Dirichlet prior on the parameters is inevitable.
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