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Lijoi, Antonio; Nipoti, Bernardo; Prünster, Igor

Bayesian inference with dependent normalized completely random measures. (English) Zbl 1309.60048

Bernoulli 20, No. 3, 1260-1291 (2014).
In the context of Bayesian inference, the authors introduce a flexible class of dependent nonparametric priors, investigate their properties and derive a sampling scheme for their implementation. The construction of the class relies on normalizing dependent completely random measures (CRM), where the dependence is created at the level of the underlying Poisson random measures (PRM). The authors provide general distributional results for the whole class of dependent CRMs and then consider analytically tractable specific priors: the bivariate Dirichlet and normalized \(\sigma\)-stable processes. The obtained analytical results form the basis for the determination of a Markov chain Monte Carlo algorithm for drawing posterior inferences, which reduces to Blackwell-MacQueen Pólya urn scheme in the univariate case. The algorithm can be used for density estimation and for analyzing the clustering structure of the data. It is illustrated through a real two-sample dataset example.
Reviewer: Pavel Stoynov (Sofia)

Cited in 39 Documents

MSC:

60G57 Random measures
62F15 Bayesian inference

Keywords:

completely random measure; dependent Poisson processes; Dirichlet process; generalized Pólya urn scheme; infinitely divisible vector; normalized \(\sigma\)-stable process; partially exchangeable random partition
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References:

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