Open Access
September 2020 Hierarchical Species Sampling Models
Federico Bassetti, Roberto Casarin, Luca Rossini
Bayesian Anal. 15(3): 809-838 (September 2020). DOI: 10.1214/19-BA1168


This paper introduces a general class of hierarchical nonparametric prior distributions which includes 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. 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 probabilistic foundation for hierarchical random measures, and allows for studying their properties under the alternative assumptions of diffuse, atomic and mixed base measure. 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 general sampling method for posterior approximation which easily accounts for non-diffuse base measures such as spike-and-slab.


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Federico Bassetti. Roberto Casarin. Luca Rossini. "Hierarchical Species Sampling Models." Bayesian Anal. 15 (3) 809 - 838, September 2020.


Published: September 2020
First available in Project Euclid: 2 October 2019

MathSciNet: MR4132651
Digital Object Identifier: 10.1214/19-BA1168

Primary: 60G09 , 60G57 , 62F15 , 62G05

Keywords: Bayesian nonparametrics , generalized species sampling , Gibbs sampling , hierarchical random measures , spike-and-slab

Vol.15 • No. 3 • September 2020
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