ABC-Hawkes: A Bayesian Approach to Parameter Estimation for the Self-exciting Hawkes Process

ABC Learning of Hawkes Processes with Missing or Noisy Event Times

The self-exciting hawkes process is widely used to model events which occur in bursts.However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion.The presence of such distortion can severely bias the learning of the parameters of the self-exciting process.To circumvent this, we propose modeling the distortionfunction explicitly.This leads to a model with an intractable likelihood function which makes it difficult to deploy standard parameter estimationtechniques.As such, we develop the abc-hawkes algorithm which is a novelapproach to estimation based on approximate bayesian computation and markov chain monte carlo.This allows the parameters of the self-exciting process to be learned in settings where conventional methods induce substantial bias or are inapplicable.