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On the Pitman–Yor process with spike and slab base measure

Author

Listed:
  • A. Canale
  • A. Lijoi
  • B. Nipoti
  • I. Prünster

Abstract

SummaryFor the most popular discrete nonparametric models, beyond the Dirichlet process, the prior guess at the shape of the data-generating distribution, also known as the base measure, is assumed to be diffuse. Such a specification greatly simplifies the derivation of analytical results, allowing for a straightforward implementation of Bayesian nonparametric inferential procedures. However, in several applied problems the available prior information leads naturally to the incorporation of an atom into the base measure, and then the Dirichlet process is essentially the only tractable choice for the prior. In this paper we fill this gap by considering the Pitman–Yor process with an atom in its base measure. We derive computable expressions for the distribution of the induced random partitions and for the predictive distributions. These findings allow us to devise an effective generalized Pólya urn Gibbs sampler. Applications to density estimation, clustering and curve estimation, with both simulated and real data, serve as an illustration of our results and allow comparisons with existing methodology. In particular, we tackle a functional data analysis problem concerning basal body temperature curves.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:3:p:681-697.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx041
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    Citations

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    Cited by:

    1. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    2. Favaro, Stefano & Panero, Francesca & Rigon, Tommaso, 2021. "Bayesian nonparametric disclosure risk assessment," LSE Research Online Documents on Economics 117305, London School of Economics and Political Science, LSE Library.
    3. 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.
    4. Lawless Caroline & Arbel Julyan, 2019. "A simple proof of Pitman–Yor’s Chinese restaurant process from its stick-breaking representation," Dependence Modeling, De Gruyter, vol. 7(1), pages 45-52, March.
    5. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
    6. Daniel R. Kowal & Antonio Canale, 2021. "Semiparametric Functional Factor Models with Bayesian Rank Selection," Papers 2108.02151, arXiv.org, revised May 2022.
    7. Laura D'Angelo & Antonio Canale & Zhaoxia Yu & Michele Guindani, 2023. "Bayesian nonparametric analysis for the detection of spikes in noisy calcium imaging data," Biometrics, The International Biometric Society, vol. 79(2), pages 1370-1382, June.
    8. 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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