IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i2d10.1007_s11009-020-09777-y.html
   My bibliography  Save this article

Point Processes on Directed Linear Networks

Author

Listed:
  • Jakob G. Rasmussen

    (Aalborg University)

  • Heidi S. Christensen

    (Aalborg University)

Abstract

In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to the setting of directed linear networks. For models specified by such a conditional intensity function, we derive an explicit expression for the likelihood function, specify two simulation algorithms (the inverse method and Ogata’s modified thinning algorithm), and consider methods for model checking through the use of residuals. We also extend the results and methods to the case of a marked point process on a directed linear network. Furthermore, we consider specific classes of point process models on directed linear networks (Poisson processes, Hawkes processes, non-linear Hawkes processes, self-correcting processes, and marked Hawkes processes), all adapted from well-known models in the temporal setting. Finally, we apply the results and methods to analyse simulated and neurological data.

Suggested Citation

  • Jakob G. Rasmussen & Heidi S. Christensen, 2021. "Point Processes on Directed Linear Networks," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 647-667, June.
  • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-020-09777-y
    DOI: 10.1007/s11009-020-09777-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09777-y
    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/s11009-020-09777-y?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. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Adrian Baddeley & Aruna Jammalamadaka & Gopalan Nair, 2014. "Multitype point process analysis of spines on the dendrite network of a neuron," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(5), pages 673-694, November.
    3. Isham, Valerie & Westcott, Mark, 1979. "A self-correcting point process," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 335-347, May.
    4. Qi Wei Ang & Adrian Baddeley & Gopalan Nair, 2012. "Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 591-617, December.
    5. Jesper Møller & Jakob G. Rasmussen, 2006. "Approximate Simulation of Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 53-64, March.
    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. Laura Anton-Sanchez & Pedro Larrañaga & Ruth Benavides-Piccione & Isabel Fernaud-Espinosa & Javier DeFelipe & Concha Bielza, 2017. "Three-dimensional spatial modeling of spines along dendritic networks in human cortical pyramidal neurons," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-14, June.
    2. Greg McSwiggan & Adrian Baddeley & Gopalan Nair, 2017. "Kernel Density Estimation on a Linear Network," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 324-345, June.
    3. Matthias Eckardt & Jorge Mateu, 2021. "Second-order and local characteristics of network intensity functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 318-340, June.
    4. Matthias Eckardt & Mehdi Moradi, 2024. "Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(2), pages 346-378, June.
    5. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    6. Kateřina Koňasová & Jiří Dvořák, 2021. "Stochastic Reconstruction for Inhomogeneous Point Patterns," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 527-547, June.
    7. Johan Debayle & Vesna Gotovac Ðogaš & Kateřina Helisová & Jakub Staněk & Markéta Zikmundová, 2021. "Assessing Similarity of Random sets via Skeletons," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 471-490, June.
    8. Jiří Dvořák & Tomáš Mrkvička, 2022. "Graphical tests of independence for general distributions," Computational Statistics, Springer, vol. 37(2), pages 671-699, April.
    9. Peter Halpin & Paul Boeck, 2013. "Modelling Dyadic Interaction with Hawkes Processes," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 793-814, October.
    10. Zhu, Lingjiong, 2013. "Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 544-550.
    11. Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    12. Møller, Jesper & Torrisi, Giovanni Luca, 2007. "The pair correlation function of spatial Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 995-1003, June.
    13. Myllymäki, Mari & Kuronen, Mikko & Bianchi, Simone & Pommerening, Arne & Mehtätalo, Lauri, 2024. "A Bayesian approach to projecting forest dynamics and related uncertainty: An application to continuous cover forests," Ecological Modelling, Elsevier, vol. 491(C).
    14. Martin Magris, 2019. "On the simulation of the Hawkes process via Lambert-W functions," Papers 1907.09162, arXiv.org.
    15. Philip A. White & Alan E. Gelfand, 2021. "Generalized Evolutionary Point Processes: Model Specifications and Model Comparison," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1001-1021, September.
    16. Dai, Wenlin & Mrkvička, Tomáš & Sun, Ying & Genton, Marc G., 2020. "Functional outlier detection and taxonomy by sequential transformations," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    17. V. Filimonov & D. Sornette, 2015. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1293-1314, August.
    18. Jesper Møller & Heidi S. Christensen & Francisco Cuevas-Pacheco & Andreas D. Christoffersen, 2021. "Structured Space-Sphere Point Processes and K-Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 569-591, June.
    19. Diquigiovanni, Jacopo & Fontana, Matteo & Vantini, Simone, 2022. "Conformal prediction bands for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    20. Johannes Wieditz & Yvo Pokern & Dominic Schuhmacher & Stephan Huckemann, 2022. "Characteristic and necessary minutiae in fingerprints," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 27-50, January.

    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:metcap:v:23:y:2021:i:2:d:10.1007_s11009-020-09777-y. 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.