MODELING NEURAL ACTIVITY USING THE GENERALIZED INVERSE GAUSSIAN DISTRIBUTION

Spike trains from neurons are often used to make inferences about the underlying processes that generate the spikes, Random walks or diffusi ons are commonly used to model these processes; in such models, a spik e corresponds to the first passage of the diffusion to a boundary, or firing threshold, An important first step in such a study is to fit fa milies of densities to the trains' interspike interval histograms; the estimated parameters, and the families' goodness of fit can then prov ide information about the process leading to the spikes, In this paper , we propose the generalized inverse Gaussian family because its membe rs arise as first passage time distributions of certain diffusions to a constant boundary, We provide some theoretical support for the use o f these diffusions in neural firing models, We compare this family wit h the lognormal family, using spike trains from retinal ganglion cells of goldfish, and simulations from an integrate-and-fire and a dynamic al model for generating spikes, We show that the generalized inverse G aussian family is closer to the true model in all these cases.