IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v112y2017i518p721-732.html
   My bibliography  Save this article

Random Partition Distribution Indexed by Pairwise Information

Author

Listed:
  • David B. Dahl
  • Ryan Day
  • Jerry W. Tsai

Abstract

We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for flexible Bayesian modeling. A defining feature of the distribution is that it allocates probability among partitions within a given number of subsets, but it does not shift probability among sets of partitions with different numbers of subsets. Our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant. The distribution of the number of subsets (and its moments) is available in closed-form and is not a function of the similarities. Our formulation has an explicit probability mass function (with a tractable normalizing constant) so the full suite of MCMC methods may be used for posterior inference. We compare our distribution with several existing partition distributions, showing that our formulation has attractive properties. We provide three demonstrations to highlight the features and relative performance of our distribution.

Suggested Citation

  • David B. Dahl & Ryan Day & Jerry W. Tsai, 2017. "Random Partition Distribution Indexed by Pairwise Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 721-732, April.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:721-732
    DOI: 10.1080/01621459.2016.1165103
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2016.1165103
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2016.1165103?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. Harshinder Singh, 2002. "Probabilistic model for two dependent circular variables," Biometrika, Biometrika Trust, vol. 89(3), pages 719-723, August.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. Lennox, Kristin P. & Dahl, David B. & Vannucci, Marina & Tsai, Jerry W., 2009. "Density Estimation for Protein Conformation Angles Using a Bivariate von Mises Distribution and Bayesian Nonparametrics," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 586-596.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wei Jin & Yang Ni & Leah H. Rubin & Amanda B. Spence & Yanxun Xu, 2022. "A Bayesian nonparametric approach for inferring drug combination effects on mental health in people with HIV," Biometrics, The International Biometric Society, vol. 78(3), pages 988-1000, September.
    2. Pierpaolo De Blasi & Ramsés H. Mena & Igor Prünster, 2022. "Asymptotic behavior of the number of distinct values in a sample from the geometric stick-breaking process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 143-165, February.

    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. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. Fernández-Durán Juan José & Gregorio-Domínguez MarÍa Mercedes, 2014. "Modeling angles in proteins and circular genomes using multivariate angular distributions based on multiple nonnegative trigonometric sums," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 1-18, February.
    3. Saptarshi Chakraborty & Samuel W. K. Wong, 2023. "On the circular correlation coefficients for bivariate von Mises distributions on a torus," Statistical Papers, Springer, vol. 64(2), pages 643-675, April.
    4. Kanti Mardia, 2010. "Bayesian analysis for bivariate von Mises distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 515-528.
    5. Miriam Aparicio, 2021. "Resiliency and Cooperation or Regarding Social and Collective Competencies for University Achievement. An Analysis from a Systemic Perspective," European Journal of Social Sciences Education and Research Articles, Revistia Research and Publishing, vol. 8, ejser_v8_.
    6. Yunpeng Zhao & Qing Pan & Chengan Du, 2019. "Logistic regression augmented community detection for network data with application in identifying autism‐related gene pathways," Biometrics, The International Biometric Society, vol. 75(1), pages 222-234, March.
    7. Wu, Han-Ming & Tien, Yin-Jing & Chen, Chun-houh, 2010. "GAP: A graphical environment for matrix visualization and cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 767-778, March.
    8. José E. Chacón, 2021. "Explicit Agreement Extremes for a 2 × 2 Table with Given Marginals," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 257-263, July.
    9. F. Marta L. Di Lascio & Andrea Menapace & Roberta Pappadà, 2024. "A spatially‐weighted AMH copula‐based dissimilarity measure for clustering variables: An application to urban thermal efficiency," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    10. Yifan Zhu & Chongzhi Di & Ying Qing Chen, 2019. "Clustering Functional Data with Application to Electronic Medication Adherence Monitoring in HIV Prevention Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(2), pages 238-261, July.
    11. Irene Vrbik & Paul McNicholas, 2015. "Fractionally-Supervised Classification," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 359-381, October.
    12. Maurizio Vichi & Carlo Cavicchia & Patrick J. F. Groenen, 2022. "Hierarchical Means Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 553-577, November.
    13. Batool, Fatima & Hennig, Christian, 2021. "Clustering with the Average Silhouette Width," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    14. Patrick D. Shay & Stephen S. Farnsworth Mick, 2017. "Clustered and distinct: a taxonomy of local multihospital systems," Health Care Management Science, Springer, vol. 20(3), pages 303-315, September.
    15. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," 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. 12(2), pages 235-260, June.
    16. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    17. Matthijs Warrens, 2010. "Inequalities Between Kappa and Kappa-Like Statistics for k×k Tables," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 176-185, March.
    18. Redivo, Edoardo & Nguyen, Hien D. & Gupta, Mayetri, 2020. "Bayesian clustering of skewed and multimodal data using geometric skewed normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    19. Jerzy Korzeniewski, 2016. "New Method Of Variable Selection For Binary Data Cluster Analysis," Statistics in Transition New Series, Polish Statistical Association, vol. 17(2), pages 295-304, June.
    20. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlasa:v:112:y:2017:i:518:p:721-732. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.