TY - JOUR

T1 - Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model

AU - Paninski, Liam

AU - Haith, Adrian

AU - Szirtes, Gabor

N1 - Funding Information:
Acknowledgements This work was partially supported by funding from the Gatsby Charitable Trust and by a Royal Society International Research Fellowship to LP. AH is funded by UK EPSRC/MRC at the Neuroinformatics Doctoral Training Centre, University of Edinburgh. We thank C.K.I. Williams for valuable conversations throughout the project and J. Fisher for helpful feedback on an early draft of the manuscript.

PY - 2008/2

Y1 - 2008/2

N2 - We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.

AB - We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.

KW - Large deviations approximation

KW - Markov process

KW - Volterra integral equation

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U2 - 10.1007/s10827-007-0042-x

DO - 10.1007/s10827-007-0042-x

M3 - Article

C2 - 17492371

AN - SCOPUS:38549175663

SN - 0929-5313

VL - 24

SP - 69

EP - 79

JO - Journal of Computational Neuroscience

JF - Journal of Computational Neuroscience

IS - 1

ER -