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A constructive definition of Dirichlet priors. (English) Zbl 0823.62007
Summary: We give a simple and new constructive definition of Dirichlet measures removing the restriction that the basic space should be \({\mathcal R}_ k\). We also give complete, self contained proofs of the three basic results for Dirichlet measures:
1. The Dirichlet measure is a probability measure on the space of all probability measures.
2. It gives probability one to the subset of discrete probability measures.
3. The posterior distribution is also a Dirichlet measure.

62B99 Sufficiency and information
62A01 Foundations and philosophical topics in statistics