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

Liam Paninski, Adrian Haith, Gabor Szirtes

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)69-79
Number of pages11
JournalJournal of Computational Neuroscience
Volume24
Issue number1
DOIs
StatePublished - Feb 2008

Keywords

  • Large deviations approximation
  • Markov process
  • Volterra integral equation

ASJC Scopus subject areas

  • Sensory Systems
  • Cognitive Neuroscience
  • Cellular and Molecular Neuroscience

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