Abstract
The Fano factor, defined as the variance-to-mean ratio of spike counts in a time window, is often used to measure the variability of neuronal spike trains. However, despite its transparent definition, careless use of the Fano factor can easily lead to distorted or even wrong results. One of the problems is the unclear dependence of the Fano factor on the spiking rate, which is often neglected or handled insufficiently. In this paper we aim to explore this problem in more detail and to study the possible solution, which is to evaluate the Fano factor in the operational time. We use equilibrium renewal and Markov renewal processes as spike train models to describe the method in detail, and we provide an illustration on experimental data.
Highlights
The frequency by which neurons generate spikes is commonly considered as a basic form of information transfer within the neuronal system (Adrian and Zotterman, 1926; Perkel and Bullock, 1968)
We studied the effect of the firing rate on the sampling Fano factor F(w)
This approach should not be confused with the study of the objective dependency of the Fano factor, F, on the firing intensity, which is described in some experimental studies and in many theoretical models
Summary
The frequency by which neurons generate spikes (action potentials) is commonly considered as a basic form of information transfer within the neuronal system (Adrian and Zotterman, 1926; Perkel and Bullock, 1968). Based on properties of Poisson distribution, as the Poisson process is some kind of template for any series of uniform events appearing in time, the index of dispersion was introduced (Cox and Lewis, 1966) It relates the variance of the number of spikes in a time window to its mean. Considering that the squared coefficient of variation is equal to the Fano factor (over an infinite window), experimental studies and countless numbers of the theoretical papers present the Fano factor as a property of the models investigated in them. Relating the variance to this quantity may induce the wrong feeling that the measure (index of dispersion, Fano factor) is firing rate independent (Figure 1) Such independence is valid only asymptotically for exceptionally fast firing and exceptionally slow firing, in both cases with respect to the time window over which the counts of spikes are investigated. A method for comparison of variability of two or more data sets with different firing rates is proposed and evaluated
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