Distribution-free graphical and statistical analysis of serial dependence in neuronal spike trains

Abstract

Two-dimensional ‘joint’ interval distributions of sequential interspike intervals (ISIs) are a commonly used tool in neuronal spike train analysis. We present and evaluate here a modification of the joint interval plot using ranked ISIs. This modification provides clearer graphical evaluation of serial dependence in ISI sequences, a distribution-free basis for isolating changes in serial dependence across experimental treatments from changes in ISI distributions, and a basis for unambiguous statistical tests of serial dependence and stationarity. To validate this method and illustrate the advantages of its use we have applied it to both single-neuron spike trains recorded from cultured mammalian spinal cord neurons and artificial spike trains generated by stochastic models with defined burst envelopes and serial dependencies.