Quantification, smoothing, and confidence limits for single-units' histograms

Abstract

In this article the relationships among firing rate, probability of firing and counts per bin are examined. It is suggested that PSTHs, autocorrelations and crosscorrelations of neuronal activity should all be expressed in units of firing rates (spikes/s), since the values obtained by such scaling are independent of bin size and of total time of measurement. A simple method for these histograms is described. Methods to compute confidence limits for PSTHs, autocorrelations and crosscorrelations are suggested. The computations are based on the null hypothesis that the spike train(s) is (are) the realization of (independent) Poisson-point process(es). The validity and the limitations of these computations methods, when applied to spike trains, are discussed. Methods to smooth out random fluctuation with little distortion of the histogram's shape are described. It is suggested that one can minimize the distortion of the histogram in the time-domain and in the frequency-domain by using a bell-shaped bin whose center point slides continuously along the histogram. The article aims at giving the potential user of the methods some insight for the meaning of the formulae. It describes in detail how the methods are applied in practice and illustrates each method by using real data from single-unit recordings.