A Bayesian Account for Estimating the Number of Neurons during Spike Sorting

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Extracellular recordings have long been an invaluable tool for understanding neural population activity. Spike sorting is the process of unmixing the contributing sources in a recording to obtain the spiking activity of individual neurons. Identifying the correct number of neurons is an error-prone process involving a considerable amount of intrinsic uncertainty. However, most spike sorting algorithms do not account for this uncertainty, but instead use a single point estimate. Using a fully probabilistic approach, we demonstrate that the point estimate leads to systematic misestimation of the number of neurons. We estimate the number of neurons present in the data by sampling from the actual posterior distribution using reversible jump Markov chain Monte Carlo, in the context of realistic ground truth data. The expected value of the probabilistic estimate is then compared to the widely used maximum a posteriori (MAP) estimate of the number of neurons. We find that even in the absence of incorrect modelling assumptions, using a point estimate leads to a systematic underestimation of the number of present neurons. This effect is visible for a wide range of values for the recording time and the noise available in the recording. More specifically, we find that decreasing noise leads to a decrease in this bias only for high sorting accuracy. If the sorting accuracy is low, this effect is reversed. Furthermore, we find that the size of the bias can initially be decreased by increasing the recording time, but for longer recordings this effect comes to a halt. Misestimating the number of neurons contributes to errors in dividing spikes into clusters, and thus impacts the clarity of the results, e.g. by fusing different neurons, or splitting single neurons. As a consequence, correlations and other estimated properties would be affected. The present results provide an analytical guide to correct for this error.
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