A New Method for Detecting Neural Interconnectivity

We propose a class of counting process models for analysing firing times of an ensemble of neurons. We allow the counting process intensities to be unspecified, unknown functions of the times passed since the most recent firings. Under this assumption we derive a class of statistics with their respective thresholds as well as graphical methods for detecting neural connectivity. We introduce a model under which detection is shown to be certain for long series of observations and suggest ways to estimate strength and classify the interactions as inhibition or excitation. The power of the proposed methods is compared by simulating observations from artificial networks. By analysing empirically obtained series we obtain results which are consistent with those obtained from cross correlation based methods but in addition obtain new insights on further aspects of the interactions.