Simulation of Stochastic Point Processes with Defined Properties

Abstract

We describe procedures that allow one to numerically simulate artificial spike trains matching real spike trains with respect to interspike interval distributions, in particular firing rates, interspike interval irregularity, and spike-count variability, and also time-varying firing rates and the corresponding properties in the nonstationary case. Spike trains recorded from neocortical neurons result from complicated interactions among very many cells. Due to a notorious lack of knowledge about the structure of the underlying network, it is currently impossible to capture the dynamical processes directly in terms of explicit biophysical models. It is useful, though, to consider abstract stochastic models that summarize all unknown details in terms of appropriate statistical ensembles. Stochastic point processes represent a useful mathematical abstraction of neuronal spike trains (see Chap. 1, this volume). Therefore, numerical simulations of point processes with defined properties are an important tool for exploration and for the reliable interpretation of measured data. Certain statistical procedures critically depend on the availability of data in a format analogous to measured data, but with well-defined probabilistic properties.