IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v204y2025ics0167947324001774.html
   My bibliography  Save this article

A Dirichlet process model for directional-linear data with application to bloodstain pattern analysis

Author

Listed:
  • Zou, Tong
  • Stern, Hal S.

Abstract

Directional data require specialized models because of the non-Euclidean nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional layer of complexity. A Bayesian nonparametric approach is introduced to analyze directional-linear data. Firstly, the projected normal distribution is extended to model the joint distribution of linear variables and a directional variable with arbitrary dimension projected from a higher-dimensional augmented multivariate normal distribution. The new distribution is called the semi-projected normal distribution (SPN) and can be used as the mixture distribution in a Dirichlet process model to obtain a more flexible class of models for directional-linear data. Then, a conditional inverse-Wishart distribution is proposed as part of the prior distribution to address an identifiability issue inherited from the projected normal and preserve conjugacy with the SPN. The SPN mixture model shows superior performance in clustering on synthetic data compared to the semi-wrapped Gaussian model. The experiments show the ability of the SPN mixture model to characterize bloodstain patterns. A hierarchical Dirichlet process model with the SPN distribution is built to estimate the likelihood of bloodstain patterns under a posited causal mechanism for use in a likelihood ratio approach to the analysis of forensic bloodstain pattern evidence.

Suggested Citation

  • Zou, Tong & Stern, Hal S., 2025. "A Dirichlet process model for directional-linear data with application to bloodstain pattern analysis," Computational Statistics & Data Analysis, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:csdana:v:204:y:2025:i:c:s0167947324001774
    DOI: 10.1016/j.csda.2024.108093
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324001774
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.108093?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. Lidong Zhang & Qikai Li & Yuanjun Guo & Zhile Yang & Lei Zhang, 2018. "An Investigation of Wind Direction and Speed in a Featured Wind Farm Using Joint Probability Distribution Methods," Sustainability, MDPI, vol. 10(12), pages 1-15, November.
    2. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Rodríguez, Carlos E. & Núñez-Antonio, Gabriel & Escarela, Gabriel, 2020. "A Bayesian mixture model for clustering circular data," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    5. Mastrantonio, Gianluca, 2018. "The joint projected normal and skew-normal: A distribution for poly-cylindrical data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 14-26.
    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. 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).
    2. 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.
    3. Evelina Gabasova & John Reid & Lorenz Wernisch, 2017. "Clusternomics: Integrative context-dependent clustering for heterogeneous datasets," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-29, October.
    4. Dong, Aqi & Melnykov, Volodymyr, 2024. "Contaminated Kent mixture model for clustering non-spherical directional data with heavy tails or scatter," Statistics & Probability Letters, Elsevier, vol. 208(C).
    5. Crook Oliver M. & Gatto Laurent & Kirk Paul D. W., 2019. "Fast approximate inference for variable selection in Dirichlet process mixtures, with an application to pan-cancer proteomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(6), pages 1-20, December.
    6. 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.
    7. 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.
    8. Michelle Dietzen & Haoran Zhai & Olivia Lucas & Oriol Pich & Christopher Barrington & Wei-Ting Lu & Sophia Ward & Yanping Guo & Robert E. Hynds & Simone Zaccaria & Charles Swanton & Nicholas McGranaha, 2024. "Replication timing alterations are associated with mutation acquisition during breast and lung cancer evolution," Nature Communications, Nature, vol. 15(1), pages 1-23, December.
    9. 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.
    10. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    11. Amiri, Babak & Karimianghadim, Ramin, 2024. "A novel text clustering model based on topic modelling and social network analysis," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    12. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    13. A van Giessen & K G M Moons & G A de Wit & W M M Verschuren & J M A Boer & H Koffijberg, 2015. "Tailoring the Implementation of New Biomarkers Based on Their Added Predictive Value in Subgroups of Individuals," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-14, January.
    14. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    15. Stefano Tonellato & Andrea Pastore, 2013. "On the comparison of model-based clustering solutions," Working Papers 2013:05, Department of Economics, University of Venice "Ca' Foscari".
    16. Elvira Pelle & Roberta Pappadà, 2021. "A clustering procedure for mixed-type data to explore ego network typologies: an application to elderly people living alone in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1507-1533, December.
    17. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    18. Parvin Ahmadi & Iman Gholampour & Mahmoud Tabandeh, 2018. "Cluster-based sparse topical coding for topic mining and document clustering," 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(3), pages 537-558, September.
    19. Tom Wilderjans & Eva Ceulemans & Iven Mechelen, 2008. "The CHIC Model: A Global Model for Coupled Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 729-751, December.
    20. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.

    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:204:y:2025:i:c:s0167947324001774. 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.