The paper titled, “Self-Exciting Point Process Models of Civilian Deaths in Iraq”, deals with fitting point processes to civilian deaths from March 2003 to December 2007. In this post, I will summarize main points from the paper

Firstly, What is “Operation Iraqi Freedom” ? Here’s a wiki blurb

The 2003 invasion of Iraq lasted from 19 March to 1 May 2003 and signaled the start of the conflict that later came to be known as the Iraq War, which was dubbed Operation Iraqi Freedom by the United States. The invasion consisted of 21 days of major combat operations, in which a combined force of troops from the United States, the United Kingdom, Australia and Poland invaded Iraq and deposed the Ba’athist government of Saddam Hussein. The invasion phase consisted primarily of a conventionally fought war which concluded with the capture of the Iraqi capital of Baghdad by American forces.

The devastating war has had dire consequences and over 100,000 Iraqi civilians have died. The authors hypothesize that the temporal events are driven by two components :

  1. Baseline rate is dependent on the region. This mean that there is Spatial heterogeneity in background rates

  2. Self-exciting mechanism : Individuals committing an initial act of violence may later return to the same or a nearby place, within a short period of time, to replicate the successes of the previous event. In other instances, an act of violence by any individual or group may incite reprisals, and counter reprisals leading to a cycle of violence.

The main aspect where the models considered in the paper departs from the usual self-exciting models is : It assumes non-stationary base line rate.Three different non-stationary processes are tested out :

  1. Step function for baseline rate

  2. Linear model for baseline rate

  3. Non-parametric estimation of baseline rate using Kernel smoothing

Since there is a nonstationary part to the baseline rate, the authors do not propose a Poisson Null model. It would be like comparing apples to oranges. Instead, the authors use a Null model as one without the self-exciting component.

The authors analyze 15,977 deaths and make the following assumptions in the analysis :

  • Bulk deaths on a day are considered as a single death event

  • No distinction is made between different types of events

  • The analysis considers only the start date and not the end date

  • Events recorded on the same day are statistically independent

The analysis examine temporal patterns of violent deaths for four different regions in Iraq including Karkh,
Najaf, Mosul, and Fallujah. For each region, the following aspects are reported :

  • How many events out of the entire dataset fall in the region  ?

  • How does AIC of a model with linear base rate + self exciting component., stack up against, AIC of null model that comprises linear baseline rate component only ?

  • How does AIC of a model with step function baseline rate + self exciting component., stack up against, AIC of null model that comprises  step function  baseline rate component only ?

  • How does AIC of a model with smoothed baseline rate component + self exciting component., stack up against AIC of null model that comprises  smoothed base rate component only ?

  • Parameter estimate that gives an idea about the # of direct offspring events

  • Average time over which an excited event to happen following a background event.

  • What % of the events are explained by baseline rate component ?

  • What % of events are explained by self-exciting component ?

The following are the findings across all regions :

  • 37%-50% of the deaths are the result of self-exciting component

  • Stationary background rate model underperforms model with a non-stationary background rate.

  • In three of the four regions examined here, including Karkh, Mosul and Fallujah, each initiating event is expected to generate slightly more than one self-excited daughter or offspring event

  • There is considerable variability in the time scales over which self-excited events occur.

Towards the end of the paper, the authors claim the importance of the results by saying,

Our results also raise the possibility that intervention strategies can be designed to counteract  self-excitation in patterns of Iraqi violence. If it is know that a large fraction of events generate daughter events, then it may be possible to strategically detect this mechanism.

For instance, if daughter events are generated out of a desire to replicate recent successes, then recognizing and altering the environmental or situational characteristics the facilitated success in the first place may help to decrease the chance of self-excitation.

Alternatively, if daughter events are driven by cycles of reprisals, then intervening with the impacted parties may decrease the chance of self-excitation. While there may be general strategies that are applicable across both types of self-excitation, such events are inherently situational and will require a situational response.