On Firing Rate Estimation for Dependent Interspike Intervals

TL;DR

This paper introduces a non-parametric method to estimate the conditional instantaneous firing rate in spike trains with dependent interspike intervals, addressing limitations of traditional methods.

Contribution

It proposes a novel non-parametric estimator for the conditional firing rate in dependent ISIs and provides an algorithm to assess its reliability.

Findings

Estimator applied successfully to simulated data from a stochastic model

Estimator validated on in vitro experimental data

Reliability and consistency of the estimator demonstrated

Abstract

If interspike intervals are dependent the instantaneous firing rate does not catch important features of spike trains. In this case the conditional instantaneous rate plays the role of the instantaneous firing rate for the case of samples of independent interspike intervals. If the conditional distribution of the interspikes intervals is unknown, it becomes difficult to evaluate the conditional firing rate. We propose a non parametric estimator for the conditional instantaneous firing rate for Markov, stationary and ergodic ISIs. An algorithm to check the reliability of the proposed estimator is introduced and its consistency properties are proved. The method is applied to data obtained from a stochastic two compartment model and to in vitro experimental data.