  We present a probabilistic model of events in continuous time in which each
event triggers a Poisson process of successor events. The ensemble of observed
events is thereby modeled as a superposition of Poisson processes. Efficient
inference is feasible under this model with an EM algorithm. Moreover, the EM
algorithm can be implemented as a distributed algorithm, permitting the model
to be applied to very large datasets. We apply these techniques to the modeling
of Twitter messages and the revision history of Wikipedia.
