Truncation thresholds: a pair of spike detection thresholds computed using truncated probability distributions

Abstract

We describe a method for computing a pair of spike detection thresholds, called 'truncation thresholds', using truncated probability distributions, for extracellular recordings. In existing methods the threshold is usually set to a multiple of an estimate of the standard deviation of the noise in the recording, with the multiplication factor being chosen between 3 and 5 according to the researcher's preferences. Our method has the following advantages over these methods. First, because the standard deviation is usually estimated from the entire recording, which includes the spikes, it increases with firing rate. By contrast, truncation thresholds decrease in absolute value with increasing firing rate, thereby capturing more of the signal. Second, the parameters of the selected noise distribution are estimated more accurately by maximum likelihood fitting of the truncated distribution to the data delimited by the truncation thresholds. Third, the computation of the truncation thresholds is completely data-driven. It does not involve a user defined multiplication factor. Fourth, methods that use a threshold that is proportional to the estimated standard deviation of the noise assume that the noise distribution is symmetrical around the mean. By contrast, truncation thresholds are not linked to each other by an assumption of symmetry about some axis. Fifth, existing methods do not verify that subthreshold data obey a noise distribution. Truncation thresholds, however, are defined by the fact that the distribution of the data they delimit is statistically indistinguishable, according to the Kolmogorov Smirnov test, from a selected distribution, truncated at those thresholds. Application of the method is illustrated using recordings from cortical area Ml in awake behaving rats, as well as in simulated recordings. Source code and executables of a software suite that computes the truncation thresholds are provided for the case when the noise distribution is modeled as truncated normal.