Stochasticity, spikes and decoding: sufficiency and utility of order statistics

For over 75 years it has been clear that the number of spikes in a neural response is an important part of the neuronal code. Starting as early as the 1950's with MacKay and McCullough, there has been speculation over whether each spike and its exact time of occurrence carry information. Although it is obvious that the firing rate carries information it has been less clear as to whether there is information in exactly timed patterns, when they arise from the dynamics of the neurons and networks, as opposed to when they represent some strong external drive that entrains them. One strong null hypothesis that can be applied is that spike trains arise from stochastic sampling of an underlying deterministic temporally modulated rate function, that is, there is a time-varying rate function. In this view, order statistics seem to provide a sufficient theoretical construct to both generate simulated spike trains that are indistinguishable from those observed experimentally, and to evaluate (decode) the data recovered from experiments. It remains to learn whether there are physiologically important signals that are not described by such a null hypothesis.