Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19.

Hawkes processes are a form of self-exciting process that has been used in numerous applications, including neuroscience, seismology, and terrorism. While these self-exciting processes have a simple formulation, they can model incredibly complex phenomena. Traditionally Hawkes processes are a continuous-time process, however we enable these models to be applied to a wider range of problems by considering a discrete-time variant of Hawkes processes.

Reconstructing the functional connectivity of multiple spike trains using Hawkes models.

Background: Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods are in the general statistical framework of the multivariate Hawkes processes. However, they usually require a huge amount of data, some prior knowledge about the recorded network, and/or may produce an increasing number of spikes along time during simulation.

Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis.

When dealing with classical spike train analysis, the practitioner often performs goodness-of-fit tests to test whether the observed process is a Poisson process, for instance, or if it obeys another type of probabilistic model (Yana et al. in Biophys. J.