## The most likely voltage path and large deviations
approximations for integrate-and-fire neurons

Journal
of Computational Neuroscience 21: 71-87.

We develop theory and numerical methods for computing the most likely
subthreshold voltage path of a noisy integrate-and-fire (IF) neuron,
given observations of the neuron's superthreshold spiking activity.
This optimal voltage path satisfies a second-order ordinary
differential (Euler-Lagrange) equation which may be solved
analytically in a number of special cases, and which may be solved
numerically in general via a simple ``shooting'' algorithm. Our
results are applicable for both linear and nonlinear subthreshold
dynamics, and in certain cases may be extended to correlated
subthreshold noise sources. We also show how this optimal voltage may
be used to: 1) help sample efficiently from the conditional
subthreshold noise distribution; 2) obtain approximations to the
likelihood that an IF cell with a given set of parameters was
responsible for the observed spike train; and 3) obtain approximations
to the instantaneous firing rate and interspike interval distribution
of a given noisy IF cell. The latter probability approximations are
based on the classical Freidlin-Wentzell theory of large deviations
principles for stochastic differential equations. We close by
comparing this most likely voltage path to the true observed
subthreshold voltage trace in a case when intracellular voltage
recordings are available * in vitro*.

Reprint (580K, pdf) | Related work on integrate-and-fire
models | Liam
Paninski's home