Integrate-and-fire model with linear escape rates . Consider a leaky integrate-and-fire neuron with linear escape rate,
(a) Start with the non-leaky integrate-and-fire model by considering the limit of . The membrane potential of the model is then
Assume constant input, set and calculate the hazard and the interval distribution.
(b) Consider the leaky integrate-and-fire model with time constant and constant input . Determine the membrane potential, the hazard and the interval distribution.
Likelihood of a spike train . In an in-vitro experiment, a time-dependent current was injected into a neuron for a time and four spikes were observed at times .
(a) What is the likelihood that this spike train could have been generated by a leaky integrate-and-fire model with linear escape rate defined in Eq. ( 9.38 )?
(b) Rewrite the likelihood in terms of the interval distribution and hazard of time-dependent renewal theory.
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