pith. sign in

arxiv: 2605.22038 · v1 · pith:NIY7FZONnew · submitted 2026-05-21 · 📊 stat.ME

A Mixed Self-Exciting Process to Model Epileptic Seizures

Karen Kanaster , Giovani L. Silva , Peter Mueller , Jacob Pellinen , Elizabeth Juarez-Colunga This is my paper

Pith reviewed 2026-05-22 04:15 UTC · model grok-4.3

classification 📊 stat.ME
keywords Hawkes processseizure clusteringepilepsymixed effectsBayesian modelrecurrent eventspoint process
0
0 comments X

The pith

A Bayesian mixed Hawkes process quantifies seizure clustering and shows bias from ignoring patient heterogeneity in epilepsy data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a self-exciting point process model for recurrent seizures that combines a background rate with an excitation boost after each event to capture clustering. Random effects and covariates are included to account for differences across the 407 patients tracked in the Human Epilepsy Project diaries over three years. Fitting produces estimates of 1.57 days between primary and secondary seizures and 2.20 seizures per cluster on average. The work further shows that models without random effects underestimate the background rate and overestimate the excitation strength when patients differ. These results matter because accurate separation of steady rates from triggered clusters can improve forecasts of seizure risk in clinical monitoring.

Core claim

We propose a Bayesian mixed Hawkes process model that addresses seizure clustering and heterogeneity between individuals. In the Hawkes process, the intensity is accelerated each time an event occurs, through the composition of background and excitation intensity functions. The proposed model incorporates a Weibull baseline intensity to model a trend in background seizure rates over time, while the excitation process accounts for seizure clustering within individuals. We model heterogeneity among individuals by including covariates and random effects in both the background and excitation intensities. In the HEP study, the average time between primary and secondary seizures within an ividuals

What carries the argument

Mixed Hawkes process intensity that adds a Weibull baseline trend to an excitation kernel, with random effects and covariates for individual heterogeneity in background and excitation.

If this is right

  • The model yields specific estimates for the average time between primary and secondary seizures of 1.57 days and 2.20 seizures per cluster.
  • Including random effects corrects for underestimation of background intensity when heterogeneity is present.
  • Including random effects corrects for overestimation of excitation rates when heterogeneity is present.
  • The approach allows individualized modeling of seizure patterns through covariates and random effects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The clustering estimates could support clinical decisions on adjusting treatment or monitoring after an observed seizure.
  • Similar mixed self-exciting models could be tested on other recurrent medical events such as migraine attacks to measure their clustering properties.
  • Replacing the Weibull baseline with other flexible time trends would test whether the self-excitation findings remain stable.

Load-bearing premise

The observed seizures arise from a self-exciting intensity that combines a smooth Weibull trend in the background rate with a decaying boost after each seizure, plus patient-specific random adjustments to those components.

What would settle it

Collect an independent set of seizure diary records from a comparable group of patients and verify whether the mean number of seizures per cluster falls within the credible interval 1.96 to 2.47.

Figures

Figures reproduced from arXiv: 2605.22038 by Elizabeth Juarez-Colunga, Giovani L. Silva, Jacob Pellinen, Karen Kanaster, Peter Mueller.

Figure 1
Figure 1. Figure 1: Daily seizure counts for random sample of 30 individuals from HEP study. Darker tick marks [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Nonparametric smoothed hazard rate estimates with 95% confidence intervals for HEP data. Event [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Posterior predictive distributions of mean total number of reported seizure events per subject, [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Posterior predictive trajectories and observed trajectory for cumulative number of reported seizure [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results of Simulation Study I for mixed Hawkes process model with covariates and random effects [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
read the original abstract

Epilepsy is a neurological disorder characterized by recurrent seizures affecting more than 70 million people worldwide. Often, an individual with epilepsy is more likely to experience subsequent seizures following an initial seizure, a process we call seizure clustering. Motivated by seizure diary data collected over three years from 407 individuals newly diagnosed with focal epilepsy in the Human Epilepsy Project (HEP), we propose a Bayesian mixed Hawkes process model that addresses seizure clustering and heterogeneity between individuals. In the Hawkes process, the intensity is accelerated each time an event occurs, through the composition of background and excitation intensity functions. The proposed model incorporates a Weibull baseline intensity to model a trend in background seizure rates over time, while the excitation process accounts for seizure clustering within individuals. We model heterogeneity among individuals by including covariates and random effects in both the background and excitation intensities. In the HEP study, the average time between primary and secondary seizures within an individual is 1.57 (95\% CrI: 1.43, 1.70) days, with an average of 2.20 (1.96, 2.47) seizures per cluster. We demonstrate that omitting random effects in the presence of heterogeneity leads to underestimation of the background intensity and overestimation of excitation rates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a Bayesian mixed Hawkes process for modeling seizure clustering and individual heterogeneity in diary data from 407 newly diagnosed focal epilepsy patients in the Human Epilepsy Project. The intensity combines a Weibull baseline trend, an excitation kernel, covariates, and random effects on both background and excitation components. Posterior summaries include an average of 1.57 days (95% CrI 1.43–1.70) between primary and secondary seizures and 2.20 seizures per cluster (1.96–2.47); a simulation study is used to show that omitting random effects underestimates background intensity and overestimates excitation rates.

Significance. If the simulation results are robust, the work supplies a practical Bayesian framework for recurrent-event data with self-excitation and unobserved heterogeneity. Explicit demonstration of bias induced by ignoring random effects is a useful methodological warning for applied Hawkes-process analyses in biostatistics and neurology.

major comments (2)
  1. [Simulation Study] Simulation study: the reported direction of bias (underestimation of background intensity, overestimation of excitation) is shown only when data are generated from the exact random-effects distribution and variance components used in the simulation. It is not demonstrated that the same bias pattern would arise under plausible alternative heterogeneity structures (heavier tails, correlation between background and excitation random effects, or time-varying heterogeneity) that might better match the HEP diaries.
  2. [Model Specification] Model definition: the precise functional form of the intensity (Weibull baseline plus excitation kernel plus random effects) and the identifiability constraints imposed on the random-effects variances are not fully specified in a single equation block. Without this, it is difficult to verify that the posterior estimates of cluster size and inter-seizure time are invariant to reparameterization.
minor comments (2)
  1. [Results] Table or figure presenting the posterior means and credible intervals for the Weibull shape/scale and excitation parameters would improve readability of the main results.
  2. [Data Description] The description of the HEP data (number of seizures per patient, observation lengths, covariate distributions) is summarized only briefly; a supplementary table with basic descriptive statistics would aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We address each major comment below with honest assessments of the current work and clear plans for revision. We believe these changes will strengthen the presentation and robustness discussion without altering the core contributions.

read point-by-point responses

  1. Referee: [Simulation Study] Simulation study: the reported direction of bias (underestimation of background intensity, overestimation of excitation) is shown only when data are generated from the exact random-effects distribution and variance components used in the simulation. It is not demonstrated that the same bias pattern would arise under plausible alternative heterogeneity structures (heavier tails, correlation between background and excitation random effects, or time-varying heterogeneity) that might better match the HEP diaries.

    Authors: We agree that the simulation demonstrates the bias specifically under the random-effects distribution and variance components used in our model. This choice was deliberate to illustrate the consequences of omitting random effects when they are present in the data-generating process, providing a direct methodological warning for applied Hawkes process analyses. While we acknowledge that additional simulations under alternative structures (e.g., heavier tails, correlated random effects, or time-varying heterogeneity) would offer broader robustness evidence, such extensions involve substantial computational cost and are unlikely to reverse the qualitative finding that ignoring heterogeneity biases background and excitation estimates. In revision, we will add an explicit discussion of this scope limitation and note that the demonstrated bias pattern is representative for the model class considered. revision: partial

  2. Referee: [Model Specification] Model definition: the precise functional form of the intensity (Weibull baseline plus excitation kernel plus random effects) and the identifiability constraints imposed on the random-effects variances are not fully specified in a single equation block. Without this, it is difficult to verify that the posterior estimates of cluster size and inter-seizure time are invariant to reparameterization.

    Authors: We thank the referee for identifying this presentational gap. The intensity function is described across sections but not consolidated. In the revised manuscript, we will add a single, self-contained equation block that explicitly defines the full intensity as the sum of the Weibull baseline, the excitation kernel, covariate terms, and the random effects on both background and excitation components. We will also state the identifiability constraints (e.g., any centering or fixed-scale assumptions on the random-effects variances) in the same block. This will make it straightforward to verify that the reported posterior summaries for cluster size and inter-seizure times remain invariant under reparameterization. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation or demonstration

full rationale

The paper defines a Bayesian mixed Hawkes process with Weibull baseline intensity, excitation kernel, covariates, and random effects for individual heterogeneity, then fits this model to the external HEP diary data to report posterior summaries such as mean inter-seizure time and cluster size. The demonstration that omitting random effects biases background and excitation estimates is performed via a standard simulation study that generates data under the fitted mixed model and refits the misspecified version; this illustrates consequences of misspecification under the paper's own assumptions rather than reducing any reported prediction or first-principles result to an input quantity by construction. No self-definitional equations, fitted-input predictions, or load-bearing self-citations that collapse the central claims are present. The derivation chain remains self-contained against the external HEP data and conventional Hawkes-process literature.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into exact parameter counts; the model relies on fitted Weibull parameters, excitation kernel parameters, random effect variances, and priors, all treated as free parameters estimated from data. No new physical entities are postulated.

free parameters (3)
  • Weibull baseline parameters
    Shape and scale parameters modeling time trend in background seizure intensity.
  • Excitation kernel parameters
    Control the magnitude and decay of self-excitation after each seizure.
  • Random effects variances
    Capture between-individual heterogeneity in both background and excitation components.
axioms (2)
  • domain assumption Seizure times follow a self-exciting point process whose intensity is the sum of a baseline and excitation terms.
    Foundational modeling choice for the Hawkes process in the abstract.
  • domain assumption Bayesian hierarchical modeling with random effects and priors is appropriate for the clustered, heterogeneous data.
    Invoked to handle individual variation and produce credible intervals.

pith-pipeline@v0.9.0 · 5765 in / 1556 out tokens · 68681 ms · 2026-05-22T04:15:32.546152+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

130 extracted references · 130 canonical work pages

  1. [1]

    Spatial Statistics , author =

    Handling missing data in self-exciting point process models , volume =. Spatial Statistics , author =. 2019 , pages =. doi:10.1016/j.spasta.2018.12.004 , abstract =

    work page doi:10.1016/j.spasta.2018.12.004 2019

  2. [2]

    Intelligent Data Analysis , author =

    Bayesian estimation of decay parameters in. Intelligent Data Analysis , author =. 2023 , pages =. doi:10.3233/IDA-216283 , abstract =

    work page doi:10.3233/ida-216283 2023

  3. [3]

    The Annals of Statistics , author =

    Nonparametric. The Annals of Statistics , author =. 2020 , file =. doi:10.1214/19-AOS1903 , language =

    work page doi:10.1214/19-aos1903 2020

  4. [4]

    , month = jun, year =

    Deutsch, Isabella and Ross, Gordon J. , month = jun, year =. arXiv preprint , publisher =

    work page

  5. [5]

    Proceedings of the AAAI Conference on Artificial Intelligence , author =

    Hawkes. Proceedings of the AAAI Conference on Artificial Intelligence , author =. 2018 , file =. doi:10.1609/aaai.v32i1.12116 , abstract =

    work page doi:10.1609/aaai.v32i1.12116 2018

  6. [6]

    Journal of Computational and Graphical Statistics , author =

    A. Journal of Computational and Graphical Statistics , author =. 2020 , pages =. doi:10.1080/10618600.2019.1617159 , abstract =

    work page doi:10.1080/10618600.2019.1617159 2020

  7. [7]

    Statistical Science , author =

    Bayesian. Statistical Science , author =. 2018 , file =. doi:10.1214/17-STS630 , abstract =

    work page doi:10.1214/17-sts630 2018

  8. [8]

    Journal of the American Statistical Association , author =

    A. Journal of the American Statistical Association , author =. 2015 , pages =. doi:10.1080/01621459.2014.969424 , language =

    work page doi:10.1080/01621459.2014.969424 2015

  9. [9]

    Journal of Computational and Graphical Statistics , author =

    Parameter. Journal of Computational and Graphical Statistics , author =. 2022 , pages =. doi:10.1080/10618600.2022.2050247 , abstract =

    work page doi:10.1080/10618600.2022.2050247 2022

  10. [10]

    Journal of Futures Markets , author =

    Hawkes. Journal of Futures Markets , author =. 2014 , pages =. doi:10.1002/fut.21644 , abstract =

    work page doi:10.1002/fut.21644 2014

  11. [11]

    and Lee, Young and Pollett, Philip K

    Laub, Patrick J. and Lee, Young and Pollett, Philip K. and Taimre, Thomas , month = may, year =. Hawkes

    work page

  12. [12]

    Epilepsia , author =

    Prospective validation study of an epilepsy seizure risk system for outpatient evaluation , volume =. Epilepsia , author =. 2020 , pages =. doi:10.1111/epi.16397 , abstract =

    work page doi:10.1111/epi.16397 2020

  13. [13]

    Epilepsia Open , author =

    Does my posterior look big in this?—. Epilepsia Open , author =. 2019 , pages =. doi:10.1002/epi4.12328 , language =

    work page doi:10.1002/epi4.12328 2019

  14. [14]

    Epilepsia , author =

    A big data approach to the development of mixed‐effects models for seizure count data , volume =. Epilepsia , author =. 2017 , pages =. doi:10.1111/epi.13727 , abstract =

    work page doi:10.1111/epi.13727 2017

  15. [15]

    Epilepsia Open , author =

    Epilepsy as a dynamic disease:. Epilepsia Open , author =. 2018 , pages =. doi:10.1002/epi4.12112 , abstract =

    work page doi:10.1002/epi4.12112 2018

  16. [16]

    Annals of Clinical and Translational Neurology , author =

    Is seizure frequency variance a predictable quantity? , volume =. Annals of Clinical and Translational Neurology , author =. 2018 , pages =. doi:10.1002/acn3.519 , abstract =

    work page doi:10.1002/acn3.519 2018

  17. [17]

    The Annals of Applied Statistics , author =

    Bayesian non-homogeneous hidden. The Annals of Applied Statistics , author =. 2023 , file =. doi:10.1214/22-AOAS1630 , language =

    work page doi:10.1214/22-aoas1630 2023

  18. [18]

    Novel study design to assess the efficacy and tolerability of antiseizure medications for focal‐onset seizures in infants and young children:

    Auvin, Stéphane and French, Jacqueline and Dlugos, Denis and Knupp, Kelly G and Perucca, Emilio and Arzimanoglou, Alexis and Whalen, Ed and Shellhaas, Renée A , file =. Novel study design to assess the efficacy and tolerability of antiseizure medications for focal‐onset seizures in infants and young children:

    work page

  19. [19]

    PLOS ONE , author =

    Simple discrete-time self-exciting models can describe complex dynamic processes:. PLOS ONE , author =. 2021 , pages =. doi:10.1371/journal.pone.0250015 , abstract =

    work page doi:10.1371/journal.pone.0250015 2021

  20. [20]

    A flexible, random histogram kernel for discrete-time

    Browning, Raiha and Rousseau, Judith and Mengersen, Kerrie , month = aug, year =. A flexible, random histogram kernel for discrete-time

    work page

  21. [21]

    Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data , abstract =

    Miscouridou, Xenia and Caron, Francois and Teh, Yee Whye , file =. Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data , abstract =

    work page

  22. [22]

    Miscouridou, Xenia and Bhatt, Samir and Mohler, George and Flaxman, Seth and Mishra, Swapnil , month = oct, year =. Cox-

    work page

  23. [23]

    emedicine.medscape.com/article/1187334-print , language =

    work page arXiv

  24. [24]

    Predicting

    Engelhard, Matthew and Xu, Hongteng and Carin, Lawrence and Oliver, Jason A and Hallyburton, Matthew and McClernon, F Joseph , year =. Predicting

    work page

  25. [25]

    Journal of the Royal Statistical Society Series C: Applied Statistics , author =

    Network. Journal of the Royal Statistical Society Series C: Applied Statistics , author =. 2022 , pages =. doi:10.1111/rssc.12581 , abstract =

    work page doi:10.1111/rssc.12581 2022

  26. [26]

    and Curley, James and Zheng, Tian , month = aug, year =

    Wu, Jing and Ward, Owen G. and Curley, James and Zheng, Tian , month = aug, year =. Markov-

    work page

  27. [27]

    Probability and random processes , isbn =

    Grimmett, Geoffrey and Stirzaker, David , year =. Probability and random processes , isbn =

    work page

  28. [28]

    Journal of Computational and Graphical Statistics , author =

    Programming with models: writing statistical algorithms for general model structures with. Journal of Computational and Graphical Statistics , author =. 2017 , pages =. doi:10.1080/10618600.2016.1172487 , number =

    work page doi:10.1080/10618600.2016.1172487 2017

  29. [29]

    and Vere-Jones, David , year =

    Daley, Daryl J. and Vere-Jones, David , year =. An introduction to the theory of point processes. 1:

    work page

  30. [30]

    Non-uniform random variate generation , isbn =

    Devroye, Luc , year =. Non-uniform random variate generation , isbn =

    work page

  31. [31]

    , year =

    Hawkes, Alan G. , year =. Spectra of. Biometrika , publisher =. doi:10.2307/2334319 , abstract =

    work page doi:10.2307/2334319

  32. [32]

    and Oakes, David , year =

    Hawkes, Alan G. and Oakes, David , year =. A. Journal of Applied Probability , publisher =. doi:10.2307/3212693 , abstract =

    work page doi:10.2307/3212693

  33. [33]

    Epilepsy Research , author =

    Long-term seizure diary tracking habits in clinical studies:. Epilepsy Research , author =. 2024 , pages =. doi:10.1016/j.eplepsyres.2024.107379 , abstract =

    work page doi:10.1016/j.eplepsyres.2024.107379 2024

  34. [34]

    Epileptic Disorders , author =

    Electronic seizure diaries for clinical care and research , volume =. Epileptic Disorders , author =. 2022 , pages =. doi:10.1684/epd.2022.1451 , abstract =

    work page doi:10.1684/epd.2022.1451 2022

  35. [35]

    Simulating recurrent events that mimic actual data: a review of the literature with emphasis on event-dependence , shorttitle =

    Pénichoux, Juliette and Moreau, Thierry and Latouche, Aurélien , month = mar, year =. Simulating recurrent events that mimic actual data: a review of the literature with emphasis on event-dependence , shorttitle =

    work page

  36. [36]

    Pediatric Neurology , author =

    Responsive. Pediatric Neurology , author =. 2023 , pages =. doi:10.1016/j.pediatrneurol.2023.03.001 , language =

    work page doi:10.1016/j.pediatrneurol.2023.03.001 2023

  37. [37]

    Seizure: European Journal of Epilepsy , author =

    Epilepsy surgery in children with genetic etiologies:. Seizure: European Journal of Epilepsy , author =. 2023 , pages =. doi:10.1016/j.seizure.2023.10.011 , abstract =

    work page doi:10.1016/j.seizure.2023.10.011 2023

  38. [38]

    Epilepsia , author =

    Leveraging expertise and optimizing clinical research:. Epilepsia , author =. 2023 , pages =. doi:10.1111/epi.17579 , abstract =

    work page doi:10.1111/epi.17579 2023

  39. [39]

    Epilepsia , author =

    Surgical evaluation in children. Epilepsia , author =. 2022 , pages =. doi:10.1111/epi.17124 , abstract =

    work page doi:10.1111/epi.17124 2022

  40. [40]

    Statistics in Medicine , author =

    Generating survival times to simulate. Statistics in Medicine , author =. 2005 , pages =. doi:10.1002/sim.2059 , abstract =

    work page doi:10.1002/sim.2059 2005

  41. [41]

    Simulation and

    Lim, Kar Wai and Lee, Young and Hanlen, Leif and Zhao, Hongbiao , month = mar, year =. Simulation and

    work page

  42. [42]

    and Lee, Young and Taimre, Thomas , year =

    Laub, Patrick J. and Lee, Young and Taimre, Thomas , year =. The. doi:10.1007/978-3-030-84639-8 , language =

    work page doi:10.1007/978-3-030-84639-8

  43. [43]

    Juarez-Colunga, E and Dean, C B , file =

    work page

  44. [44]

    and Lawless, Jerald F

    Cook, Richard J. and Lawless, Jerald F. , year =. The statistical analysis of recurrent events , isbn =

    work page

  45. [45]

    Therapy , author =

    Post-traumatic epilepsy: an overview , volume =. Therapy , author =. 2010 , pages =. doi:10.2217/thy.10.57 , abstract =

    work page doi:10.2217/thy.10.57 2010

  46. [46]

    Epilepsia , author =

    Standards for epidemiologic studies and surveillance of epilepsy , volume =. Epilepsia , author =. 2011 , pages =. doi:10.1111/j.1528-1167.2011.03121.x , abstract =

    work page doi:10.1111/j.1528-1167.2011.03121.x 2011

  47. [47]

    Methodology and Computing in Applied Probability , author =

    Bayesian. Methodology and Computing in Applied Probability , author =. 2013 , pages =. doi:10.1007/s11009-011-9272-5 , abstract =

    work page doi:10.1007/s11009-011-9272-5 2013

  48. [48]

    Epilepsia Open , author =

    Management of post‐traumatic epilepsy:. Epilepsia Open , author =. 2017 , pages =. doi:10.1002/epi4.12049 , abstract =

    work page doi:10.1002/epi4.12049 2017

  49. [49]

    Obral, Katarzyna , file =. A

    work page

  50. [50]

    Methodology and Computing in Applied Probability , author =

    Approximate. Methodology and Computing in Applied Probability , author =. 2006 , pages =. doi:10.1007/s11009-006-7288-z , abstract =

    work page doi:10.1007/s11009-006-7288-z 2006

  51. [51]

    Advances in Applied Probability , author =

    Perfect simulation of. Advances in Applied Probability , author =. 2005 , pages =. doi:10.1239/aap/1127483739 , abstract =

    work page doi:10.1239/aap/1127483739 2005

  52. [52]

    On the simulation of the

    Magris, Martin , month = jul, year =. On the simulation of the

    work page

  53. [53]

    Methodology and Computing in Applied Probability , author =

    Hawkes. Methodology and Computing in Applied Probability , author =. 2022 , pages =. doi:10.1007/s11009-022-09938-1 , abstract =

    work page doi:10.1007/s11009-022-09938-1 2022

  54. [54]

    and Wong, Victoria and Nurse, Ewan S

    Hannon, Timothy and Fernandes, Kiran M. and Wong, Victoria and Nurse, Ewan S. and Cook, Mark J. , month = mar, year =. Over- and underreporting of seizures:. Epilepsia , publisher =. doi:10.1111/epi.17930 , abstract =

    work page doi:10.1111/epi.17930

  55. [55]

    Rasmussen, Jakob Gulddahl , month = jun, year =. Lecture

    work page

  56. [56]

    Electronic Communications in Probability , author =

    Exact simulation of. Electronic Communications in Probability , author =. 2013 , file =. doi:10.1214/ECP.v18-2717 , abstract =

    work page doi:10.1214/ecp.v18-2717 2013

  57. [57]

    Acta Paediatrica , author =

    Tracking epilepsy with an electronic diary , volume =. Acta Paediatrica , author =. 2010 , pages =. doi:10.1111/j.1651-2227.2010.01694.x , language =

    work page doi:10.1111/j.1651-2227.2010.01694.x 2010

  58. [58]

    Epilepsia , author =

    Focal nonmotor versus motor seizures:. Epilepsia , author =. 2020 , pages =. doi:10.1111/epi.16707 , abstract =

    work page doi:10.1111/epi.16707 2020

  59. [59]

    Fifty years later: new directions in. SORT. Statistics and Operations Research Transactions , author =. 2022 , pages =. doi:10.2436/20.8080.02.116 , abstract =

    work page doi:10.2436/20.8080.02.116 2022

  60. [60]

    Constructing

    Choi, Edward and Du, Nan and Chen, Robert and Song, Le and Sun, Jimeng , month = nov, year =. Constructing. 2015. doi:10.1109/ICDM.2015.144 , abstract =

    work page doi:10.1109/icdm.2015.144 2015

  61. [61]

    Journal of the American Statistical Association , author =

    Self-. Journal of the American Statistical Association , author =. 2011 , pages =. doi:10.1198/jasa.2011.ap09546 , language =

    work page doi:10.1198/jasa.2011.ap09546 2011

  62. [62]

    International Journal of Forecasting , author =

    Hawkes process modeling of. International Journal of Forecasting , author =. 2022 , pages =. doi:10.1016/j.ijforecast.2021.07.001 , abstract =

    work page doi:10.1016/j.ijforecast.2021.07.001 2022

  63. [63]

    The Lancet , author =

    Epilepsy in adults , volume =. The Lancet , author =. 2019 , pages =. doi:10.1016/S0140-6736(18)32596-0 , language =

    work page doi:10.1016/s0140-6736(18)32596-0 2019

  64. [64]

    Brain and Behavior , author =

    The burden of epilepsy and unmet need in people with focal seizures , volume =. Brain and Behavior , author =. 2022 , pages =. doi:10.1002/brb3.2589 , abstract =

    work page doi:10.1002/brb3.2589 2022

  65. [65]

    Epilepsia , author =

    The prevalence of epilepsy and pharmacoresistant epilepsy in adults:. Epilepsia , author =. 2008 , pages =. doi:10.1111/j.1528-1167.2008.01579.x , abstract =

    work page doi:10.1111/j.1528-1167.2008.01579.x 2008

  66. [66]

    Neurobiology of Disease , author =

    Long-term seizure dynamics are determined by the nature of seizures and the mutual interactions between them , volume =. Neurobiology of Disease , author =. 2021 , pages =. doi:10.1016/j.nbd.2021.105347 , abstract =

    work page doi:10.1016/j.nbd.2021.105347 2021

  67. [67]

    Nature Communications , author =

    Critical slowing down as a biomarker for seizure susceptibility , volume =. Nature Communications , author =. 2020 , pages =. doi:10.1038/s41467-020-15908-3 , abstract =

    work page doi:10.1038/s41467-020-15908-3 2020

  68. [68]

    Nature Communications , author =

    Multi-day rhythms modulate seizure risk in epilepsy , volume =. Nature Communications , author =. 2018 , pages =. doi:10.1038/s41467-017-02577-y , abstract =

    work page doi:10.1038/s41467-017-02577-y 2018

  69. [69]

    Disease Models & Mechanisms , author =

    Semiology, clustering, periodicity and natural history of seizures in an experimental occipital cortical epilepsy model , copyright =. Disease Models & Mechanisms , author =. 2018 , pages =. doi:10.1242/dmm.036194 , abstract =

    work page doi:10.1242/dmm.036194 2018

  70. [70]

    Brain , author =

    Interictal spikes and epileptic seizures: their relationship and underlying rhythmicity , volume =. Brain , author =. 2016 , pages =. doi:10.1093/brain/aww019 , language =

    work page doi:10.1093/brain/aww019 2016

  71. [71]

    Epilepsia , author =

    Seizure. Epilepsia , author =. 2005 , pages =. doi:10.1111/j.0013-9580.2005.29004.x , abstract =

    work page doi:10.1111/j.0013-9580.2005.29004.x 2005

  72. [72]

    Frontiers in Neurology , author =

    The. Frontiers in Neurology , author =. 2014 , file =. doi:10.3389/fneur.2014.00217 , abstract =

    work page doi:10.3389/fneur.2014.00217 2014

  73. [73]

    Experimental Neurology , author =

    Endogenous multidien rhythm of epilepsy in rats , volume =. Experimental Neurology , author =. 2019 , pages =. doi:10.1016/j.expneurol.2019.02.006 , abstract =

    work page doi:10.1016/j.expneurol.2019.02.006 2019

  74. [74]

    Epilepsia , author =

    Seizure. Epilepsia , author =. 1991 , pages =. doi:10.1111/j.1528-1157.1991.tb04703.x , abstract =

    work page doi:10.1111/j.1528-1157.1991.tb04703.x 1991

  75. [75]

    Statistical

    Ogata, Yosihiko , year =. Statistical. Journal of the American Statistical Association , publisher =. doi:10.2307/2288914 , abstract =

    work page doi:10.2307/2288914

  76. [76]

    Physical Review E , author =

    Hawkes process model with a time-dependent background rate and its application to high-frequency financial data , volume =. Physical Review E , author =. 2017 , keywords =. doi:10.1103/PhysRevE.96.012303 , abstract =

    work page doi:10.1103/physreve.96.012303 2017

  77. [77]

    Journal of Quantitative Criminology , author =

    Terrorism. Journal of Quantitative Criminology , author =. 2013 , pages =. doi:10.1007/s10940-012-9181-y , abstract =

    work page doi:10.1007/s10940-012-9181-y 2013

  78. [78]

    SN Computer Science , author =

    Sports. SN Computer Science , author =. 2025 , pages =. doi:10.1007/s42979-025-03939-w , abstract =

    work page doi:10.1007/s42979-025-03939-w 2025

  79. [79]

    Real-time analysis of neuronal firing patterns via

    Gerencser, Laszlo and Perczel, Gyorgy , month = oct, year =. Real-time analysis of neuronal firing patterns via. 2021 55th. doi:10.1109/IEEECONF53345.2021.9723129 , abstract =

    work page doi:10.1109/ieeeconf53345.2021.9723129 2021

  80. [80]

    Mohler, George and Raje, Rajeev and Carter, Jeremy and Valasik, Matthew and Brantingham, Jeffrey , month = oct, year =. A. 2018. doi:10.1109/SMC.2018.00421 , abstract =

    work page doi:10.1109/smc.2018.00421 2018

Showing first 80 references.