Clustering structure for species sampling sequences with general base\n measure

2019/08/28 by Federico Bassetti, Lucia Ladelli, Bassetti, Federico +1
Computer Science · Mathematics · #60C05 #60G09 #Advanced Clustering Algorithms Research #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1908.10727

openalex publication_date 2019/08/28 · openalex created_date 2022/09/11 · openalex updated_date 2026/07/28

Abstract

We investigate the clustering structure of species sampling sequences\n(\ξ_n)_n, with general base measure. Such sequences are exchangeable with a\nspecies sampling random probability as directing measure. The clustering\nproperties of these sequences are interesting for Bayesian nonparametrics\napplications, where mixed base measures are used, for example, to accommodate\nsharp hypotheses in regression problems and provide sparsity. In this paper, we\nprove a stochastic representation for (\ξ_n)_n in terms of a latent\nexchangeable random partition. We provide explicit expression of the EPPF of\nthe partition generated by (\ξ_n)_n in terms of the EPPF of the latent\npartition. We investigate the asymptotic behaviour of the total number of\nblocks and of the number of blocks with fixed cardinality in the partition\ngenerated by (\ξ_n)_n.\n

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• Sample Size Dependent Species Models
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