Computing likelihoods in the stochastic integrate-and-fire model: numerical methods

Recent work has examined the estimation of models of stimulus-driven neural activity in which a linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent after-current. We have formulated this problem in terms of maximum likelihood estimation: a full discussion of the problem is contained in [1, 3]). Here we present detailed numerical methods related to computing the likelihood function using the Fokker-Planck equation, excerpted from [2]. This model was first applied to neuronal data in [4].