Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants

Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants

We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of...

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Main Authors: Privault, Nicolas, Thieullen, Michèle
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Multivariant Analysis
Sensitivity Analysis
Online Access:https://hdl.handle.net/10356/170798
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1707982023-10-09T15:34:38Z Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants Privault, Nicolas Thieullen, Michèle School of Physical and Mathematical Sciences Science::Mathematics Multivariant Analysis Sensitivity Analysis We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of the model over time and to estimate the probability densities of neuronal membrane potentials using Gram-Charlier expansions. Our results are shown to provide a better alternative to Monte Carlo estimates via stochastic simulations and computer codes based on combinatorial recursions are included. Ministry of Education (MOE) Published version This research is supported by the Ministry of Education, Singapore, under its Tier 1 Grant No. MOE2020-T1-002-047. 2023-10-09T08:29:52Z 2023-10-09T08:29:52Z 2022 Journal Article Privault, N. & Thieullen, M. (2022). Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants. Physical Review E, 106(5-1), 054410-. https://dx.doi.org/10.1103/PhysRevE.106.054410 2470-0045 https://hdl.handle.net/10356/170798 10.1103/PhysRevE.106.054410 36559454 2-s2.0-85142780170 5-1 106 054410 en MOE2020-T1-002-047 Physical Review E © 2022 American Physical Society. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1103/PhysRevE.106.054410 application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Multivariant Analysis
Sensitivity Analysis
spellingShingle Science::Mathematics
Multivariant Analysis
Sensitivity Analysis
Privault, Nicolas
Thieullen, Michèle
Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
description We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of the model over time and to estimate the probability densities of neuronal membrane potentials using Gram-Charlier expansions. Our results are shown to provide a better alternative to Monte Carlo estimates via stochastic simulations and computer codes based on combinatorial recursions are included.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Privault, Nicolas
Thieullen, Michèle
format Article
author Privault, Nicolas
Thieullen, Michèle
author_sort Privault, Nicolas
title Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
title_short Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
title_full Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
title_fullStr Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
title_full_unstemmed Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
title_sort closed-form modeling of neuronal spike train statistics using multivariate hawkes cumulants
publishDate 2023
url https://hdl.handle.net/10356/170798
_version_ 1781793667951886336

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