The most likely voltage path and large deviations approximations for integrateandfire neurons
 Liam Paninski
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We develop theory and numerical methods for computing the most likely subthreshold voltage path of a noisy integrateandfire (IF) neuron, given observations of the neuron’s superthreshold spiking activity. This optimal voltage path satisfies a secondorder ordinary differential (EulerLagrange) 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 obtain approximations to (1) the likelihood that an IF cell with a given set of parameters was responsible for the observed spike train; and (2) the instantaneous firing rate and interspike interval distribution of a given noisy IF cell. The latter probability approximations are based on the classical FreidlinWentzell 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.
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 Title
 The most likely voltage path and large deviations approximations for integrateandfire neurons
 Journal

Journal of Computational Neuroscience
Volume 21, Issue 1 , pp 7187
 Cover Date
 20060801
 DOI
 10.1007/s1082700672004
 Print ISSN
 09295313
 Online ISSN
 15736873
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Likelihood
 Stochastic dynamics
 FreidlinWentzell
 Calculus of variations
 Intracellular recordings
 Industry Sectors
 Authors

 Liam Paninski ^{(1)}
 Author Affiliations

 1. Department of Statistics, Columbia University, Columbia