Modeling Neuronal Firing in Epilepsy: Fitting Hawkes Processes to Single-Unit Activity

  • György Perczel
  • Loránd Erőss
  • Dániel Fabó
  • László GerencsérEmail author
  • Zsuzsanna Vágó
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


Forecasting seizures based on information extracted from neuronal firing has a great potential in controlling closed-loop neurostimulators. For the description of neuronal firing patterns we use self-exiting point processes or Hawkes processes. In fitting them to simulated data, using a large variety of models, we consider both computability and reliability issues related to the maximum likelihood estimation (MLE) method. The models are classified via a single parameter related to stability regimes. The dependence of the accuracy of the individual parameter estimates on different regimes will be explored. We demonstrate the applicability of the MLE method to discriminate between different models with high confidence.



This research has been partially supported by the European Union, co-financed by the European Social Fund (EFOP-3.6.3-VEKOP-16-2017-00002).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • György Perczel
    • 1
    • 2
  • Loránd Erőss
    • 1
    • 2
  • Dániel Fabó
    • 1
    • 2
  • László Gerencsér
    • 3
    Email author
  • Zsuzsanna Vágó
    • 4
  1. 1.National Institute of Clinical NeurosciencesBudapestHungary
  2. 2.Faculty of Information Technology and BionicsPázmány Péter Catholic UniversityBudapestHungary
  3. 3.Systems and Control LabInstitute for Computer Science and ControlBudapestHungary
  4. 4.Faculty of Information Technology and BionicsPázmány Péter Catholic UniversityBudapestHungary

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