Hierarchical species sampling models
Federico Bassetti, Roberto Casarin, Luca Rossini · Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) · 2020
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.