Statistical Coupling Between Time Point-Processes

The observation of physical phenomena often goes through the recording of discrete time series of events, that can be represented with marked point processes. The robust estimation of the correlation between two point processes can, therefore, unveil physical mechanisms underlying the observed phenomena. However, the robust estimation of correlation between two, or more, point-processes is hindered by the signal noise (leading to false and missing point detections), the important density of points, and possible time-shift between coupled points. We propose a statistical framework that uses hypothesis testing to estimate coupling between time point-processes. Using simulations, we show that our framework accurately estimates the coupling between two time point-processes even for noisy signal (with false point detections), for high density of points and in the presence of a time shift between coupled points. By applying our statistical framework to the recordings of neuron population activity in mouse visual cortex, we measure the functional coupling between individual neurons, and cluster neurons into functional ensembles.