Fokker-Planck and Fortet equation-based parameter estimation for a leaky integrate-and-fire model with sinusoidal and stochastic forcing

Alexandre Iolov; Susanne Ditlevsen; Andrë Longtin

doi:10.1186/2190-8567-4-4

Fokker-Planck and Fortet equation-based parameter estimation for a leaky integrate-and-fire model with sinusoidal and stochastic forcing

Alexandre Iolov, Susanne Ditlevsen, Andrë Longtin

Institut for Matematiske Fag

10 Citationer (Scopus)

1367 Downloads (Pure)

Abstract

Analysis of sinusoidal noisy leaky integrate-and-fire models and comparison with experimental data are important to understand the neural code and neural synchronization and rhythms. In this paper, we propose two methods to estimate input parameters using interspike interval data only. One is based on numerical solutions of the Fokker–Planck equation, and the other is based on an integral equation, which is fulfilled by the interspike interval probability density. This generalizes previous methods tailored to stationary data to the case of time-dependent input. The main contribution is a binning method to circumvent the problems of nonstationarity, and an easy-to-implement initializer for the numerical procedures. The methods are compared on simulated data

Originalsprog	Engelsk
Artikelnummer	4
Tidsskrift	Journal of Mathematical Neuroscience
Vol/bind	4
Udgave nummer	4
Antal sider	30
ISSN	2190-8567
DOI	https://doi.org/10.1186/2190-8567-4-4
Status	Udgivet - 2014

Adgang til dokumentet

10.1186/2190-8567-4-4

Fokker-Planck and Fortet equation-based parameter estimation for a leaky integrate-and-fire model with sinusoidal and stochastic forcingForlagets udgivne version, 2,98 MB

Citationsformater

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AB - Analysis of sinusoidal noisy leaky integrate-and-fire models and comparison with experimental data are important to understand the neural code and neural synchronization and rhythms. In this paper, we propose two methods to estimate input parameters using interspike interval data only. One is based on numerical solutions of the Fokker–Planck equation, and the other is based on an integral equation, which is fulfilled by the interspike interval probability density. This generalizes previous methods tailored to stationary data to the case of time-dependent input. The main contribution is a binning method to circumvent the problems of nonstationarity, and an easy-to-implement initializer for the numerical procedures. The methods are compared on simulated data

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