Generalized Chinese restaurant construction of exchangeable Gibbs partitions and related results

Details Generalized Chinese restaurant construction of exchangeable Gibbs partitions and related results Generalized Chinese restaurant construction of exchangeable Gibbs partitions and related results

2008-05-26

arxiv.org/abs/0805.3853v1

Mathematics

Probability

12 pages

Scientific paper

By resorting to sequential constructions of exchangeable random partitions (Pitman, 2006), and exploiting some known facts about generalized Stirling numbers, we derive a generalized Chinese restaurant process construction of exchangeable Gibbs partitions of type $\alpha$ (Gnedin and Pitman, 2006). Our construction represents the natural theoretical probabilistic framework in which to embed some recent results about a Bayesian nonparametric treatment of estimation problems arising in genetic experiment under Gibbs, species sampling, models priors.

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