Conjugacy as a Distinctive Feature of the Dirichlet Process |
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| Authors: | LANCELOT F. JAMES,ANTONIO LIJOI, IGOR PRÜ NSTER |
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| Affiliation: | Department of Information Systems and Management, Hong Kong University of Science and Technology; Dipartimento di Economia Politica e Metodi Quantitativi, Universitàdegli Studi di Pavia and CNR-IMATI, Milano; Dipartimento di Statistica e Matematica Applicata and ICER, Universitàdegli Studi di Torino |
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| Abstract: | Abstract. Recently the class of normalized random measures with independent increments, which contains the Dirichlet process as a particular case, has been introduced. Here a new technique for deriving moments of these random probability measures is proposed. It is shown that, a priori , most of the appealing properties featured by the Dirichlet process are preserved. When passing to posterior computations, we obtain a characterization of the Dirichlet process as the only conjugate member of the whole class of normalized random measures with independent increments. |
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| Keywords: | Bayesian non-parametrics conjugacy Dirichlet process increasing Lévy process normalized random measure with independent increments predictive distribution |
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