We present a generative model for representing and reasoning about the relationships among events in continuous time. We apply the model to the domain of networked and distributed computing environments where we fit the parameters of the model from timestamp observations, and then use hypothesis testing to discover dependencies between the events and changes in behavior for monitoring and diagnosis. After introducing the model, we present an EM algorithm for fitting the parameters and then present the hypothesis testing approach for both dependence discovery and change-point detection. We validate the approach for both tasks using real data from a trace of network events at Microsoft Research Cambridge. Finally, we formalize the relationship between the proposed model and the noisy-or gate for cases when time can be discretized.