Mean instantaneous firing frequency is always higher than the firing rate
Neural Computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input
Biological Cybernetics
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Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t1 and of a diffusion process conditioned to cross the boundary for the first time at t1. This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences.