Traditional waveform based spike sorting yields biased rate code estimates.

Much of neuroscience has to do with relating neural activity and behavior or environment. One common measure of this relationship is the firing rates of neurons as functions of behavioral or environmental parameters, often called tuning functions and receptive fields. Firing rates are estimated from the spike trains of neurons recorded by electrodes implanted in the brain. Individual neurons' spike trains are not typically readily available, because the signal collected at an electrode is often a mixture of activities from different neurons and noise. Extracting individual neurons' spike trains from voltage signals, which is known as spike sorting, is one of the most important data analysis problems in neuroscience, because it has to be undertaken prior to any analysis of neurophysiological data in which more than one neuron is believed to be recorded on a single electrode. All current spike-sorting methods consist of clustering the characteristic spike waveforms of neurons. The sequence of first spike sorting based on waveforms, then estimating tuning functions, has long been the accepted way to proceed. Here, we argue that the covariates that modulate tuning functions also contain information about spike identities, and that if tuning information is ignored for spike sorting, the resulting tuning function estimates are biased and inconsistent, unless spikes can be classified with perfect accuracy. This means, for example, that the commonly used peristimulus time histogram is a biased estimate of the firing rate of a neuron that is not perfectly isolated. We further argue that the correct conceptual way to view the problem out is to note that spike sorting provides information about rate estimation and vice versa, so that the two relationships should be considered simultaneously rather than sequentially. Indeed we show that when spike sorting and tuning-curve estimation are performed in parallel, unbiased estimates of tuning curves can be recovered even from imperfectly sorted neurons.