Handling missing data in self-exciting point process models

Self-exciting point processes have been applied to a wide variety of applications to understand event rates and clustering as a function of time and space. Typically, estimation procedures require a full temporal history of the data and do not handle cases where some of the history of the process is missing and unobserved. However, in many applications data collection is non-persistent resulting in known intervals of time where events of the process are unobserved. Motivated by these situations, a Bayesian estimation procedure for self-exciting point processes with missing histories is developed. The method naturally handles the missing data mechanism probabilistically through a specific step and is demonstrated on simulated data and a real conflict monitoring data where records over a period of time have been lost.