Probability distributions of the logarithm of inter-spike intervals yield accurate entropy estimates from small datasets

The maximal information that the spike train of any neuron can pass on to subsequent neurons can be quantified as the neuronal firing pattern entropy. Difficulties associated with estimating entropy from small datasets have proven an obstacle to the widespread reporting of firing pattern entropies and more generally, the use of information theory within the neuroscience community. In the most accessible class of entropy estimation techniques, spike trains are partitioned linearly in time and entropy is estimated from the probability distribution of firing patterns within a partition. Ample previous work has focused on various techniques to minimize the finite dataset bias and standard deviation of entropy estimates from under-sampled probability distributions on spike timing events partitioned linearly in time. In this manuscript we present evidence that all distribution-based techniques would benefit from inter-spike intervals being partitioned in logarithmic time. We show that with logarithmic partitioning, firing rate changes become independent of firing pattern entropy. We delineate the entire entropy estimation process with two example neuronal models, demonstrating the robust improvements in bias and standard deviation that the logarithmic time method yields over two widely used linearly partitioned time approaches.