Nonparametric Bayesian Modelling of Event Data

Gordon Ross (University of St Andrews)

Many human and physical processes give rise to event data, consisting of the times at which particular types of events occur. Examples include the spatio-temporal occurrence of earthquakes the times at which people send emails and post on social media, and the occurrence times of solar flares omitted from the sun.

These varied processes often have two features which must be modelled: 1) events follow a seasonal/periodic temporal pattern, 2) events often occur in bursts/clusters. We present a fully nonparametric Bayesian version of the self exciting Hawkes process which is able to model such event data. A flexible Dirichlet Process (DP) prior is used to model the seasonal inhomogenous background rate of a point process with a further DP being used to model the structure of bursts process behaviour which creates clustering. Various applications are then discussed.