Statistical Analysis of a Spike Train Distance in Poisson Models

Several spike train metrics have been proposed in the last years for the evaluation of neural responses. In this letter, we perform deep statistical analysis on an important metric. This metric evaluates the dissimilarity between spike trains by applying a linear filter on the trains and then integrating the squared difference of the result. The statistical analysis is made when the metric is used to evaluate spike trains originated from nonhomogenous Poisson processes. Contrary to previous works, the analytical results have been obtained for the general case and not only for particular limiting conditions. By computing the expected value of the metric, insightful information is retrieved; it allows for the proposal of a normalization factor which addresses several deficiencies when comparing neural responses.