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As a tool for capturing irregular temporal dependencies (rather thanresorting to binning temporal observations to construct time series), Hawkesprocesses with exponential decay have seen widespread adoption across manyapplication domains, such as predicting the occurrence time of the nextearthquake or stock market spike. However, practical applications of Hawkesprocesses face a noteworthy challenge: There is substantial and oftenunquantified variance in decay parameter estimations, especially in the case ofa small number of observations or when the dynamics behind the observed datasuddenly change. We empirically study the cause of these practical challengesand we develop an approach to surface and thereby mitigate them. In particular,our inspections of the Hawkes process likelihood function uncover theproperties of the uncertainty when fitting the decay parameter. We thus proposeto explicitly capture this uncertainty within a Bayesian framework. With aseries of experiments with synthetic and real-world data from domains such as"classical" earthquake modeling or the manifestation of collective emotions onTwitter, we demonstrate that our proposed approach helps to quantifyuncertainty and thereby to understand and fit Hawkes processes in practice.

Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels