Estimating Neuronal Information: Logarithmic Binning of Neuronal Inter-Spike Intervals.

Neurons communicate via the relative timing of all-or-none biophysical signals called spikes. For statistical analysis, the time between spikes can be accumulated into inter-spike interval histograms. Information theoretic measures have been estimated from these histograms to assess how information varies across organisms, neural systems, and disease conditions. Because neurons are computational units that, to the extent they process time, work not by discrete clock ticks but by the exponential decays of numerous intrinsic variables, we propose that neuronal information measures scale more naturally with the logarithm of time. For the types of inter-spike interval distributions that best describe neuronal activity, the logarithm of time enables fewer bins to capture the salient features of the distributions. Thus, discretizing the logarithm of inter-spike intervals, as compared to the inter-spike intervals themselves, yields histograms that enable more accurate entropy and information estimates for fewer bins and less data. Additionally, as distribution parameters vary, the entropy and information calculated from the logarithm of the inter-spike intervals are substantially better behaved, e.g., entropy is independent of mean rate, and information is equally affected by rate gains and divisions. Thus, when compiling neuronal data for subsequent information analysis, the logarithm of the inter-spike intervals is preferred, over the untransformed inter-spike intervals, because it yields better information estimates and is likely more similar to the construction used by nature herself.