IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v33y2024i1d10.1007_s10260-023-00726-w.html
   My bibliography  Save this article

Locating $$\gamma$$ γ -ray sources on the celestial sphere via modal clustering

Author

Listed:
  • Anna Montin

    (University of Padova)

  • Alessandra R. Brazzale

    (University of Padova)

  • Giovanna Menardi

    (University of Padova)

  • Andrea Sottosanti

    (University of Padova)

Abstract

Sky surveys represent the fundamental data basis for detecting and locating as yet undiscovered celestial objects. Since 2008, the Fermi LAT Collaboration has catalogued thousands of $$\gamma$$ γ -ray sources with the aim of extending our knowledge of the highly energetic physical mechanisms and processes that lie at the core of our Universe. In this article, we present a nonparametric clustering algorithm which identifies high-energy astronomical sources using the spatial information of the $$\gamma$$ γ -ray photons detected by the large area telescope onboard the Fermi spacecraft. In particular, the sources are identified using a von Mises–Fisher kernel estimate of the photon count density on the unit sphere via an adjustment of the mean-shift algorithm which accounts for the directional nature of the collected data and the need of local smoothing. This choice entails a number of desirable benefits. It allows us to bypass the difficulties inherent on the borders of any projection of the photon directions onto a 2-dimensional plane, while guaranteeing high flexibility. The smoothing parameter is chosen adaptively, by combining scientific input with optimal selection guidelines, as known from the literature. Using statistical tools from hypothesis testing and classification, we furthermore present an automatic way to skim off sound candidate sources from the $$\gamma$$ γ -ray emitting diffuse background and to quantify their significance. We calibrate and test our algorithm on simulated count maps provided by the Fermi LAT Collaboration.

Suggested Citation

  • Anna Montin & Alessandra R. Brazzale & Giovanna Menardi & Andrea Sottosanti, 2024. "Locating $$\gamma$$ γ -ray sources on the celestial sphere via modal clustering," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(1), pages 153-172, March.
  • Handle: RePEc:spr:stmapp:v:33:y:2024:i:1:d:10.1007_s10260-023-00726-w
    DOI: 10.1007/s10260-023-00726-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-023-00726-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10260-023-00726-w?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. Christopher R. Genovese & Marco Perone-Pacifico & Isabella Verdinelli & Larry Wasserman, 2016. "Non-parametric inference for density modes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 99-126, January.
    2. Di Marzio, Marco & Fensore, Stefania & Panzera, Agnese & Taylor, Charles C., 2019. "Kernel density classification for spherical data," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 23-29.
    3. Giovanna Menardi, 2016. "A Review on Modal Clustering," International Statistical Review, International Statistical Institute, vol. 84(3), pages 413-433, December.
    4. Abramson, Ian S., 1982. "Arbitrariness of the pilot estimator in adaptive kernel methods," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 562-567, December.
    5. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," 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. 16(3), pages 761-796, September.
    6. Arnone, Eleonora & Ferraccioli, Federico & Pigolotti, Clara & Sangalli, Laura M., 2022. "A roughness penalty approach to estimate densities over two-dimensional manifolds," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    7. Alessandro Casa & Giovanna Menardi, 2022. "Nonparametric semi-supervised classification with application to signal detection in high energy physics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 531-550, September.
    8. Bai, Z. D. & Rao, C. Radhakrishna & Zhao, L. C., 1988. "Kernel estimators of density function of directional data," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 24-39, October.
    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. Arthur Pewsey & Eduardo García-Portugués, 2021. "Rejoinder on: 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 76-82, March.
    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. Stanislav Nagy & Houyem Demni & Davide Buttarazzi & Giovanni C. Porzio, 2024. "Theory of angular depth for classification of directional data," 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. 18(3), pages 627-662, September.
    4. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate data," 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. 17(2), pages 323-345, June.
    5. Jose Ameijeiras-Alonso & Jochen Einbeck, 2024. "A fresh look at mean-shift based modal 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. 18(4), pages 1067-1095, December.
    6. Alessandro Casa & Giovanna Menardi, 2022. "Nonparametric semi-supervised classification with application to signal detection in high energy physics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 531-550, September.
    7. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 732-740.
    8. Kim, Yoon Tae & Park, Hyun Suk, 2013. "Geometric structures arising from kernel density estimation on Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 112-126.
    9. Stanislav Zámečník & Ivana Horová & Stanislav Katina & Kamila Hasilová, 2024. "An adaptive method for bandwidth selection in circular kernel density estimation," Computational Statistics, Springer, vol. 39(4), pages 1709-1728, June.
    10. Fabian Dunker & Konstantin Eckle & Katharina Proksch & Johannes Schmidt-Hieber, 2017. "Tests for qualitative features in the random coefficients model," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 225, Courant Research Centre PEG.
    11. Graciela Boente & Daniela Rodriguez & Wenceslao González Manteiga, 2014. "Goodness-of-fit Test for Directional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 259-275, March.
    12. Pham Ngoc, Thanh Mai, 2019. "Adaptive optimal kernel density estimation for directional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 248-267.
    13. Alessandro Casa & Luca Scrucca & Giovanna Menardi, 2021. "Better than the best? Answers via model ensemble in density-based 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. 15(3), pages 599-623, September.
    14. Healy, Dennis M. & Hendriks, Harrie & Kim, Peter T., 1998. "Spherical Deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 1-22, October.
    15. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
    16. Charles C. Taylor & Kanti V. Mardia & Marco Di Marzio & Agnese Panzera, 2012. "Validating protein structure using kernel density estimates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2379-2388, July.
    17. Konstantin Eckle & Nicolai Bissantz & Holger Dette & Katharina Proksch & Sabrina Einecke, 2018. "Multiscale inference for a multivariate density with applications to X-ray astronomy," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 647-689, June.
    18. Stefano Magrini, 2007. "Analysing Convergence through the Distribution Dynamics Approach: Why and how?," Working Papers 2007_13, Department of Economics, University of Venice "Ca' Foscari".
    19. Agostinelli, Claudio, 2007. "Robust estimation for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5867-5875, August.
    20. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.

    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:spr:stmapp:v:33:y:2024:i:1:d:10.1007_s10260-023-00726-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.