IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v149y2020ics0167947320300505.html
   My bibliography  Save this article

Bayesian nonparametric test for independence between random vectors

Author

Listed:
  • Ma, Zichen
  • Hanson, Timothy E.

Abstract

A nonparametric approach for testing independence among groups of continuous random variables is proposed. Gaussian-centered multivariate finite Polya tree priors are used to model the underlying probability distributions. Integrating out the random probability measure, a tractable empirical Bayes factor is derived and used as the test statistic. The Bayes factor is consistent in the sense that it tends to infinity under the alternative, and zero under the null. A p-value is then obtained through a permutation test based on the observed Bayes factor. Through a series of simulation studies, the performance of the proposed approach is examined and compared to several existing approaches based on the power of the test as well as the observed Bayes factor. Lastly, the proposed method is applied to a set of real data in ecology.

Suggested Citation

  • Ma, Zichen & Hanson, Timothy E., 2020. "Bayesian nonparametric test for independence between random vectors," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    • Handle: RePEc:eee:csdana:v:149:y:2020:i:c:s0167947320300505
    DOI: 10.1016/j.csda.2020.106959
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947320300505
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2020.106959?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. Daniel J. Benjamin & James O. Berger, 2019. "Three Recommendations for Improving the Use of p-Values," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 186-191, March.
    2. repec:bla:biomet:v:71:y:2015:i:4:p:1101-1110 is not listed on IDEAS
    3. Susan M. Paddock, 2002. "Bayesian nonparametric multiple imputation of partially observed data with ignorable nonresponse," Biometrika, Biometrika Trust, vol. 89(3), pages 529-538, August.
    4. Stephen Walker & Bani K. Mallick, 1999. "A Bayesian Semiparametric Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 55(2), pages 477-483, June.
    5. Walker S. & Damien P. & Lenk P., 2004. "On Priors With a Kullback-Leibler Property," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 404-408, January.
    6. Berger J. O & Guglielmi A., 2001. "Bayesian and Conditional Frequentist Testing of a Parametric Model Versus Nonparametric Alternatives," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 174-184, March.
    7. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, October.
    8. 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.
    9. Li Ma & Jialiang Mao, 2019. "Fisher Exact Scanning for Dependency," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 245-258, January.
    10. Ruth Heller & Yair Heller & Malka Gorfine, 2013. "A consistent multivariate test of association based on ranks of distances," Biometrika, Biometrika Trust, vol. 100(2), pages 503-510.
    11. Adam J. Branscum & Timothy E. Hanson, 2008. "Bayesian Nonparametric Meta‐Analysis Using Polya Tree Mixture Models," Biometrics, The International Biometric Society, vol. 64(3), pages 825-833, September.
    12. Bharath, Karthik & Dey, Dipak K., 2011. "Test to distinguish a Brownian motion from a Brownian bridge using Polya tree process," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 140-145, January.
    13. 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.
    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. 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.
    2. 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.
    3. Adam J. Branscum & Timothy E. Hanson, 2008. "Bayesian Nonparametric Meta‐Analysis Using Polya Tree Mixture Models," Biometrics, The International Biometric Society, vol. 64(3), pages 825-833, September.
    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. Peter Müeller & Fernando A. Quintana & Garritt Page, 2018. "Nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 175-206, June.
    6. Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.
    7. 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.
    8. 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.
    9. Rafael Carvalho Ceregatti & Rafael Izbicki & Luis Ernesto Bueno Salasar, 2021. "WIKS: a general Bayesian nonparametric index for quantifying differences between two populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 274-291, March.
    10. 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.
    11. Geurt Jongbloed & Frank H. van der Meulen & Lixue Pang, 2022. "Bayesian nonparametric estimation in the current status continuous mark model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1329-1352, September.
    12. Li, Li & Hanson, Timothy E., 2014. "A Bayesian semiparametric regression model for reliability data using effective age," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 177-188.
    13. Satoshi Morita & Peter Müller & Hiroyasu Abe, 2021. "A semiparametric Bayesian approach to population finding with time‐to‐event and toxicity data in a randomized clinical trial," Biometrics, The International Biometric Society, vol. 77(2), pages 634-648, June.
    14. Jianchang Lin & Debajyoti Sinha & Stuart Lipsitz & Adriano Polpo, 2012. "Semiparametric Bayesian Survival Analysis using Models with Log-linear Median," Biometrics, The International Biometric Society, vol. 68(4), pages 1136-1145, December.
    15. William Cipolli & Timothy Hanson, 2019. "Supervised learning via smoothed Polya trees," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 877-904, December.
    16. S Gorsky & L Ma, 2022. "Multi-scale Fisher’s independence test for multivariate dependence [A simple measure of conditional dependence]," Biometrika, Biometrika Trust, vol. 109(3), pages 569-587.
    17. Damien, Paul & Galenko, Alexander & Popova, Elmira & Hanson, Timothy, 2007. "Bayesian semiparametric analysis for a single item maintenance optimization," European Journal of Operational Research, Elsevier, vol. 182(2), pages 794-805, October.
    18. Yang, Mingan & Hanson, Timothy & Christensen, Ronald, 2008. "Nonparametric Bayesian estimation of a bivariate density with interval censored data," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5202-5214, August.
    19. Bharath, Karthik & Dey, Dipak K., 2011. "Test to distinguish a Brownian motion from a Brownian bridge using Polya tree process," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 140-145, January.
    20. Bibhas Chakraborty, 2020. "Statistical Remedies for Medical Researchers," International Statistical Review, International Statistical Institute, vol. 88(3), pages 802-804, 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:149:y:2020:i:c:s0167947320300505. 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.