IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v180y2023ics0167947322002456.html
   My bibliography  Save this article

Polya tree Monte Carlo method

Author

Listed:
  • Zhuang, Haoxin
  • Diao, Liqun
  • Yi, Grace Y.

Abstract

Markov Chain Monte Carlo (MCMC) methods have been widely used in Statistics and machine learning research. However, such methods have several limitations, including slow convergence and the inefficiency in handling multi-modal distributions. To overcome these limitations of MCMC methods, a new, efficient sampling method has been proposed and it applies to general distributions including multi-modal ones or those having complex structure. The proposed approach, called the Polya tree Monte Carlo (PTMC) method, roots in constructing a Polya tree distribution using the idea of Monte Carlo method, and then using this distribution to approximate and facilitate sampling from a target distribution that may be complex or have multiple modes. The associated convergence property of the PTMC method is established and computationally efficient sampling algorithms are developed based on the PTMC. Extensive numerical studies demonstrate the satisfactory performance of the proposed method under various settings including its superiority to the usual MCMC algorithms. The evaluation and comparison are carried out in terms of sampling efficiency, computational speed and the capacity of identifying distribution modes. Additional details about the method, proofs and simulation results are provided in the Supplementary Web Appendices online.

Suggested Citation

  • Zhuang, Haoxin & Diao, Liqun & Yi, Grace Y., 2023. "Polya tree Monte Carlo method," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002456
    DOI: 10.1016/j.csda.2022.107665
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322002456
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107665?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tore Selland Kleppe, 2016. "Adaptive Step Size Selection for Hessian-Based Manifold Langevin Samplers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 788-805, September.
    2. Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
    3. Stephen G. Walker & Bani K. Mallick, 1997. "Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 845-860.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Yuhui & Hanson, Timothy E., 2014. "Bayesian nonparametric k-sample tests for censored and uncensored data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 335-346.
    2. Levine, Richard A. & Fan, Juanjuan & Strickland, Pamela Ohman & Demirel, Shaban, 2012. "Frailty modeling via the empirical Bayes–Hastings sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1303-1318.
    3. Ernesto San Martín & Alejandro Jara & Jean-Marie Rolin & Michel Mouchart, 2011. "On the Bayesian Nonparametric Generalization of IRT-Type Models," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 385-409, July.
    4. Jianjun Zhang & Lei Yang & Xianyi Wu, 2019. "Polya tree priors and their estimation with multi-group data," Statistical Papers, Springer, vol. 60(3), pages 849-875, June.
    5. Komárek, Arnost & Lesaffre, Emmanuel, 2008. "Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3441-3458, March.
    6. Adam Branscum & Timothy Hanson & Ian Gardner, 2008. "Bayesian non-parametric models for regional prevalence estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(5), pages 567-582.
    7. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    8. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    9. Thomas A. Murray & Peter F. Thall & Ying Yuan & Sarah McAvoy & Daniel R. Gomez, 2017. "Robust Treatment Comparison Based on Utilities of Semi-Competing Risks in Non-Small-Cell Lung Cancer," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 11-23, January.
    10. Nalini Ravishanker & Dipak K. Dey, 2000. "Multivariate Survival Models with a Mixture of Positive Stable Frailties," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 293-308, September.
    11. Angela Schörgendorfer & Adam J. Branscum & Timothy E. Hanson, 2013. "A Bayesian Goodness of Fit Test and Semiparametric Generalization of Logistic Regression with Measurement Data," Biometrics, The International Biometric Society, vol. 69(2), pages 508-519, June.
    12. Shinya Sugawara, 2017. "Firm‐Driven Management of Longevity Risk: Analysis of Lump‐Sum Forward Payments in Japanese Nursing Homes," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 26(1), pages 169-204, February.
    13. Song Zhang & Peter Müller & Kim-Anh Do, 2010. "A Bayesian Semiparametric Survival Model with Longitudinal Markers," Biometrics, The International Biometric Society, vol. 66(2), pages 435-443, June.
    14. Haiming Zhou & Timothy Hanson & Jiajia Zhang, 2017. "Generalized accelerated failure time spatial frailty model for arbitrarily censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 495-515, July.
    15. Meijuan Li & Cavan Reilly & Tim Hanson, 2010. "Association Tests for a Censored Quantitative Trait and Candidate Genes in Structured Populations with Multilevel Genetic Relatedness," Biometrics, The International Biometric Society, vol. 66(3), pages 925-933, September.
    16. Cipolli III, William & Hanson, Timothy & McLain, Alexander C., 2016. "Bayesian nonparametric multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 64-79.
    17. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    18. Jiajia Zhang & Timothy Hanson & Haiming Zhou, 2019. "Bayes factors for choosing among six common survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 361-379, April.
    19. 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.
    20. Kyu Ha Lee & Virginie Rondeau & Sebastien Haneuse, 2017. "Accelerated failure time models for semi‐competing risks data in the presence of complex censoring," Biometrics, The International Biometric Society, vol. 73(4), pages 1401-1412, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002456. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.