Skellam process with resetting: a neural spike train model

Abstract

This paper introduces the Skellam process with resetting. Resetting is a modification that accommodates the modeling of neural spike trains. We show this as a biologically plausible model, which codes the information content of neural spike trains with three, potentially, time-varying functions. We show that the interspike interval distribution under this model follows a mixture of gamma distributions, a flexible class covering a wide range of commonly used models. Through simulation studies and the analyses of connected retinal ganglion and lateral geniculate nucleus cells, we evaluate the performance of this model. Copyright © 2016 John Wiley & Sons, Ltd.

A Multivariate Point Process Model for Simultaneously Recorded Neural Spike Trains

“…. , p to be estimated from the data, as was done in the univariate SPR model of [15]. The challenge is to perform parameter estimation under this more complicated model without sacrificing computational efficiency.…”

“…Following Definitions 1 and 2, and the parameterization of [15], the two parameters of the marginal SPR for neuron i are λ…”

“…The statistical modelling of neural spike trains falls under the general framework of point processes. Among point processes, the (inhomogeneous) Poisson process is a popular choice [1,14], but its theoretical properties fail to address biological phenomena such as refractoriness and burst spiking activities [15]. Furthermore, the Poisson process has very limited multivariate generalizations in terms of dependence structure [12,9,4,11,6,7].…”

“…The Skellam process with resetting (SPR) is a point process recently developed to model spike trains collected from an individual neuron [15]. A Skellam process {S(t), t ≥ 0} is defined as the difference between two independent Poisson processes, i.e.…”

“…Thus, resetting refers to bringing the path of the Skellam process back to state 0 after each spike, i.e. after each record of the process, to mimic the refractoriness of neurons [15]. In this paper we generalize the results of [15] and introduce the multivariate Skellam process with resetting (MSPR) for the analysis of simultaneously recorded spike trains from multiple neurons.…”