** Authors:**
MURAT OKATAN, MEHMET KOCATÜRK

** 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 M1 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.

** Keywords: **
Biomedical signal processing, brain-machine interfaces,
microelectrode recordings, computational neuroscience

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