Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
Neurons and Cognition
2022-11-30 v1 Probability
Statistics Theory
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2210.15549,
title = {Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants},
author = {Nicolas Privault and Michèle Thieullen},
journal= {arXiv preprint arXiv:2210.15549},
year = {2022}
}