Neuronal noise in the output can be described as a stochastic firing intensity, or escape rate, which depends on the momentary distance of the membrane potential from the threshold. The concept of escape rate can be applied to a large class of generalized integrate-and-fire models. An SRM with exponential escape rate is particularly attractive for several reasons. First, experimental data suggest an exponential escape rate (Fig. 9.3). Second, a wide spectrum of subthreshold effects can be captured by the linear filters of the SRM (Chapter 6). Third, when driven with a noisy input, nonlinear neuron models such as the AdEx can be well approximated by the SRM with exponential escape noise (Fig. 9.9). Fourth, the explicit formulas for the likelihood of an observed spike train (Section 9.2) enable a rapid fit of the neuron model to experimental data, using the concept of Generalized Linear Models to be discussed in the next chapter.

Escape noise gives rise to variability in spike firing even if the input is perfectly known. It can therefore be linked to intrinsic noise sources such as channel noise. However, more generally, any unknown component of the input which may for example arise from stochastic spike arrival can also be approximated by an appropriate escape rate function (Section 9.4). Thus the escape rate provides a phenomenological noise model that summarizes effects of biophysical channel noise as well as stochastic input.

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