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Inner spike and slab Bayesian nonparametric models

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  • Canale, Antonio
  • Lijoi, Antonio
  • Nipoti, Bernardo
  • Prünster, Igor

Abstract

Discrete Bayesian nonparametric models whose expectation is a convex linear combination of a point mass at some point of the support and a diffuse probability distribution allow to incorporate strong prior information, while still being extremely flexible. Recent contributions in the statistical literature have successfully implemented such a modelling strategy in a variety of applications, including density estimation, nonparametric regression and model-based clustering. A thorough study is presented on a large class of nonparametric models, named inner spike and slab hNRMI models and obtained by considering homogeneous normalized random measures with independent increments (hNRMI) with base measure given by a convex linear combination of a point mass and a diffuse probability distribution. In turn, the distributional properties of these models are investigated, with focus on: i) the exchangeable partition probability function they induce, ii) the distribution of the number of distinct values in an exchangeable sample, iii) the posterior predictive distribution, and iv) the distribution of the number of elements that coincide with the only point of the support with positive probability. These theoretical findings represent the main building block for an actual implementation of Bayesian inner spike and slab hNRMI models by means of a generalized Pólya urn scheme.

Suggested Citation

  • Canale, Antonio & Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2023. "Inner spike and slab Bayesian nonparametric models," Econometrics and Statistics, Elsevier, vol. 27(C), pages 120-135.
    • Handle: RePEc:eee:ecosta:v:27:y:2023:i:c:p:120-135
    DOI: 10.1016/j.ecosta.2021.10.017
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    1. Bruno Scarpa & David B. Dunson, 2009. "Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors," Biometrics, The International Biometric Society, vol. 65(3), pages 772-780, September.
    2. 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.
    3. Dunson, David B. & Herring, Amy H. & Engel, Stephanie M., 2008. "Bayesian Selection and Clustering of Polymorphisms in Functionally Related Genes," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 534-546, June.
    4. Michele Guindani & Nuno Sepúlveda & Carlos Daniel Paulino & Peter Müller, 2014. "A Bayesian semiparametric approach for the differential analysis of sequence counts data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(3), pages 385-404, April.
    5. Yang, Mingan, 2012. "Bayesian variable selection for logistic mixed model with nonparametric random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2663-2674.
    6. 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).
    7. Kim‐Anh Do & Peter Müller & Feng Tang, 2005. "A Bayesian mixture model for differential gene expression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 627-644, June.
    8. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    9. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 105-120, March.
    10. A. Canale & A. Lijoi & B. Nipoti & I. Prünster, 2017. "On the Pitman–Yor process with spike and slab base measure," Biometrika, Biometrika Trust, vol. 104(3), pages 681-697.
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