Hierarchical Species Sampling Models

Federico Bassetti, Roberto Casarin, Luca Rossini

Research output: Contribution to JournalArticleAcademic

Abstract

This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The proposed framework provides a general probabilistic foundation for hierarchical random measures with either atomic or mixed base measures and allows for studying their properties, such as the distribution of the marginal and total number of clusters. We show that hierarchical species sampling models have a Chinese Restaurants Franchise representation and can be used as prior distributions to undertake Bayesian nonparametric inference. We provide a method to sample from the posterior distribution together with some numerical illustrations. Our class of priors includes some new hierarchical mixture priors such as the hierarchical Gnedin measures, and other well-known prior distributions such as the hierarchical Pitman-Yor and the hierarchical normalized random measures.
Original languageEnglish
JournalarXiv.org
Publication statusPublished - 30 Jan 2019

Fingerprint

Prior distribution
Random Measure
Model
Random Probability Measure
Nonparametric Inference
Bayesian Nonparametrics
Number of Clusters
Posterior distribution
Class

Keywords

  • stat.ME
  • math.ST
  • stat.TH

Cite this

Bassetti, Federico ; Casarin, Roberto ; Rossini, Luca. / Hierarchical Species Sampling Models. In: arXiv.org. 2019.
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Hierarchical Species Sampling Models. / Bassetti, Federico; Casarin, Roberto; Rossini, Luca.

In: arXiv.org, 30.01.2019.

Research output: Contribution to JournalArticleAcademic

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AU - Casarin, Roberto

AU - Rossini, Luca

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AB - This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The proposed framework provides a general probabilistic foundation for hierarchical random measures with either atomic or mixed base measures and allows for studying their properties, such as the distribution of the marginal and total number of clusters. We show that hierarchical species sampling models have a Chinese Restaurants Franchise representation and can be used as prior distributions to undertake Bayesian nonparametric inference. We provide a method to sample from the posterior distribution together with some numerical illustrations. Our class of priors includes some new hierarchical mixture priors such as the hierarchical Gnedin measures, and other well-known prior distributions such as the hierarchical Pitman-Yor and the hierarchical normalized random measures.

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M3 - Article

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Bassetti F, Casarin R, Rossini L. Hierarchical Species Sampling Models. arXiv.org. 2019 Jan 30.