On the spike train variability characterized by variance-to-mean power relationship

TL;DR

This paper introduces a statistical method to model spike train variability using a variance-to-mean power relationship, enabling flexible characterization of neural firing patterns across different brain regions.

Contribution

It presents a novel model linking spike train variance and mean via a power function, with a maximum likelihood inference method for analyzing rate-modulated spike trains.

Findings

The model captures diverse variability patterns in simulated data.

Application to experimental data demonstrates the method's effectiveness.

The approach generalizes traditional Poisson assumptions.

Abstract

We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship, and based on this a maximum likelihood method is developed for inferring the parameters from rate-modulated spike trains. The proposed method is illustrated on simulated and experimental spike trains.