Inference for stochastic neuronal models
Applied Mathematics and Computation
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Minimal Models of Adapted Neuronal Response to In Vivo–lLike Input Currents
Neural Computation
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input
Biological Cybernetics
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Lapicque’s 1907 paper: from frogs to integrate-and-fire
Biological Cybernetics
Practical estimation of high dimensional stochastic differential mixed-effects models
Computational Statistics & Data Analysis
Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process
Journal of Computational Neuroscience
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Stochastic leaky integrate-and-fire (LIF) neuronal models are common theoretical tools for studying properties of real neuronal systems. Experimental data of frequently sampled membrane potential measurements between spikes show that the assumption of constant parameter values is not realistic and that some (random) fluctuations are occurring. In this article, we extend the stochastic LIF model, allowing a noise source determining slow fluctuations in the signal. This is achieved by adding a random variable to one of the parameters characterizing the neuronal input, considering each interspike interval (ISI) as an independent experimental unit with a different realization of this random variable. In this way, the variation of the neuronal input is split into fast (within-interval) and slow (between-intervals) components. A parameter estimation method is proposed, allowing the parameters to be estimated simultaneously over the entire data set. This increases the statistical power, and the average estimate over all ISIs will be improved in the sense of decreased variance of the estimator compared to previous approaches, where the estimation has been conducted separately on each individual ISI. The results obtained on real data show good agreement with classical regression methods.