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Kernel stick-breaking processes

Author

Listed:
  • David B. Dunson
  • Ju-Hyun Park

Abstract

We propose a class of kernel stick-breaking processes for uncountable collections of dependent random probability measures. The process is constructed by first introducing an infinite sequence of random locations. Independent random probability measures and beta-distributed random weights are assigned to each location. Predictor-dependent random probability measures are then constructed by mixing over the locations, with stick-breaking probabilities expressed as a kernel multiplied by the beta weights. Some theoretical properties of the process are described, including a covariate-dependent prediction rule. A retrospective Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using a simulated example and an epidemiological application. Copyright 2008, Oxford University Press.

Suggested Citation

  • David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:2:p:307-323
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    File URL: http://hdl.handle.net/10.1093/biomet/asn012
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    Citations

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    Cited by:

    1. Laura Liu, 2018. "Density Forecasts in Panel Data Models : A Semiparametric Bayesian Perspective," Finance and Economics Discussion Series 2018-036, Board of Governors of the Federal Reserve System (U.S.).
    2. Mahdi Hosseinpouri & Majid Jafari Khaledi, 2019. "An area-specific stick breaking process for spatial data," Statistical Papers, Springer, vol. 60(1), pages 199-221, February.
    3. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    4. Igari, Ryosuke & Hoshino, Takahiro, 2018. "A Bayesian data combination approach for repeated durations under unobserved missing indicators: Application to interpurchase-timing in marketing," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 150-166.
    5. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    6. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    7. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
    8. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    9. Miller, Jeffrey W., 2019. "An elementary derivation of the Chinese restaurant process from Sethuraman’s stick-breaking process," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 112-117.
    10. Yeonseung Chung & David Dunson, 2011. "The local Dirichlet process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 59-80, February.
    11. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 1-31, February.
    12. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    13. Zhang, Jianjun & Qiu, Chunjuan & Wu, Xianyi, 2018. "Bayesian ratemaking with common effects modeled by mixture of Polya tree processes," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 87-94.
    14. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
    15. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
    16. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    17. Gutiérrez, Luis & Mena, Ramsés H. & Ruggiero, Matteo, 2016. "A time dependent Bayesian nonparametric model for air quality analysis," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 161-175.
    18. Hatjispyros, Spyridon J. & Merkatas, Christos & Nicoleris, Theodoros & Walker, Stephen G., 2018. "Dependent mixtures of geometric weights priors," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 1-18.
    19. Chung, Hwan & Chang, Hsiu-Ching, 2012. "Bayesian approaches to the model selection problem in the analysis of latent stage-sequential process," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4097-4110.
    20. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    21. repec:jss:jstsof:40:i05 is not listed on IDEAS
    22. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    23. Ilenia Epifani & Antonio Lijoi, 2009. "Nonparametric Priors for Vectors of Survival Functions," Quaderni di Dipartimento 098, University of Pavia, Department of Economics and Quantitative Methods.
    24. Huang, Yifan & Meng, Shengwang, 2020. "A Bayesian nonparametric model and its application in insurance loss prediction," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 84-94.

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