Modelling ISIL terror attacks and their fatality rates with a Bayesian reversible jump marked point process

This paper attempts to find different time periods since ISIL's formation in 2013 in which the rate of ISIL attacks or their effectiveness in terms of fatalities differ. A Bayesian model is presented for marked point process data that separates the time scale into disjoint intervals as a function of the rate of the attacks and the average number of fatalities for each attack which are the marks for the model. The model is endowed with priors to discourage intervals with few events and borrow strength among rates and intensities of adjacent intervals and uses the reversible jump approach introduced by Green (1996) to allow the number of intervals to vary as a function of the rates and intensities of attacks. Application results show that the hazard of an ISIL attack has increased drastically since 6/8/2014 since they took Mosul and again increased after 2/23/16, which corresponds with major military intervention.