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Mixture of Species Sampling Models

Author

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  • Federico Bassetti

    (Department of Mathematics, Politecnico of Milano, 20133 Milano, Italy
    These authors contributed equally to this work.)

  • Lucia Ladelli

    (Department of Mathematics, Politecnico of Milano, 20133 Milano, Italy
    These authors contributed equally to this work.)

Abstract

We introduce mixtures of species sampling sequences (mSSS) and discuss how these sequences are related to various types of Bayesian models. As a particular case, we recover species sampling sequences with general (not necessarily diffuse) base measures. These models include some “spike-and-slab” non-parametric priors recently introduced to provide sparsity. Furthermore, we show how mSSS arise while considering hierarchical species sampling random probabilities (e.g., the hierarchical Dirichlet process). Extending previous results, we prove that mSSS are obtained by assigning the values of an exchangeable sequence to the classes of a latent exchangeable random partition. Using this representation, we give an explicit expression of the Exchangeable Partition Probability Function of the partition generated by an mSSS. Some special cases are discussed in detail—in particular, species sampling sequences with general base measures and a mixture of species sampling sequences with Gibbs-type latent partition. Finally, we give explicit expressions of the predictive distributions of an mSSS.

Suggested Citation

  • Federico Bassetti & Lucia Ladelli, 2021. "Mixture of Species Sampling Models," Mathematics, MDPI, vol. 9(23), pages 1-27, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3127-:d:695028
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    References listed on IDEAS

    as
    1. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97, March.
    2. Bassetti, Federico & Ladelli, Lucia, 2020. "Asymptotic number of clusters for species sampling sequences with non-diffuse base measure," Statistics & Probability Letters, Elsevier, vol. 162(C).
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    Cited by:

    1. Ali Amiryousefi & Ville Kinnula & Jing Tang, 2022. "Bayes in Wonderland! Predictive Supervised Classification Inference Hits Unpredictability," Mathematics, MDPI, vol. 10(5), pages 1-11, March.
    2. Emanuele Dolera, 2022. "Preface to the Special Issue on “Bayesian Predictive Inference and Related Asymptotics—Festschrift for Eugenio Regazzini’s 75th Birthday”," Mathematics, MDPI, vol. 10(15), pages 1-4, July.

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