Note: I filled in for J.D. Tucker on this talk. Self-exciting temporal point processes, such as Hawkes processes, are present in many application areas, including epidemiology, seismology, and surveillance, and require a consistent obser- vation period to accurately model. However, during the observation period, intervals can occur where data is not collected, either through design or malfunction. These intervals of missing data can be problematic, as they can e?ect the modeling of the point process. In this work, we present a Bayesian estimation technique to model univariate, self-exciting temporal point processes with known intervals of missing data. This technique provides a more accurate estimation of the intensity function and provides prediction-informed sensing. We compare our model to current models on simulated data and data from the Global Terrorism Database and show predictive performance improvement.