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I was looking at some attack count data in Ukraine for different days. The data is gathered from the ACCLED dataset, and there is a picture below. The picture shows individual attacks, but I can apply a grid and count the number of attacks in each region to get a rough estimate of frequency within a given grid cell. However my goal was to predict the probability contours of an attack over the areas adjacent to the attack sites. In other words, if an attack happens at a specific latitude, longitude locations, then there is a heightened risk of attack in the surrounding region over the next few days or weeks.

enter image description here

I have time series data, so I could technically look at the rise and fall in events over time in a given region and its adjacent regions and estimate the time excitation rate and the spatial decay rate. But before I go reinventing the wheel, I figured that models for such processes must exist.

Does anyone know what kind of model I would use for something like this? I also looked at GeoStatistical models and kriging--basically thinking of interpolation as a way to model the diffusion of risk around the points. One idea is to use "Indicator Kriging" where there is a 1 for an event cell and 0 for other cells, and then to krig the probability of events. I could also apply a partial differential equation model and essentially diffuse and advect the count "spikes" into the adjacent geographic region. I could use the time series data to estimate the diffusion and advection parameters. So there are lot of ideas, but I was just wondering if anyone know some common approaches.

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    $\begingroup$ A common approach is to use self-exciting point processes. $\endgroup$
    – Andy W
    Apr 14 at 18:15
  • $\begingroup$ @AndyW yes, thanks for the suggestion. I have seen these hawkes process models used for count data before. I will certainly take a look at the article. $\endgroup$
    – krishnab
    Apr 14 at 18:23
  • $\begingroup$ This isn't exactly identical, but there's a paper titled "Causal inference with spatio-temporal data: estimating the effects of airstrikes on insurgent violence in Iraq" by Georgia Papadogeorgou that may be of interest $\endgroup$
    – Adrian
    Apr 15 at 17:35
  • $\begingroup$ @Adrian thanks for the paper suggestion. I will definitely take a look. $\endgroup$
    – krishnab
    Apr 15 at 18:51

2 Answers 2

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This is not an answer, but rather a side comment:

Keep in mind that the new attacks are not independent of the previous ones. Historical data is not necessarily relevant for the future. It is probably worth thinking of the problem in the terms similar to the frames of survivorship bias: the fact that Kyiv was (unsuccessfully) attacked in the past does not necessarily make it more susceptible to the attacks in the future, maybe even the other way around, it is not worth further attacks, as the Russian army concluded by retreating. But this approach also has a flaw, as it assumes a rational actor that learns from mistakes, whereas Russia is not necessarily a rational actor. I'd be cautious with using historical data for such extrapolations.

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    $\begingroup$ (+1) Your points about independence and sampling bias are quite salient. In some sense the conflict in Ukraine is a partial information game, but one in which expected utility theory cannot be used reliably since the participants of the 'game' are not necessarily rational. I am not sure prospect theory nicely applies either since people's way of assessing financial risk may not be the same as war strategists... $\endgroup$
    – Galen
    Apr 14 at 21:08
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    $\begingroup$ This was the same thought that popped up in my mind. But the question gets less strong in the second half and it is more like the question: Is it more likely that the next attack is in the vicinity of the last attack or attacks? The points that we see in the map could have been attacked in a completely random order, but also it might be that they occur in clusters. $\endgroup$
    – Sextus Empiricus
    Apr 14 at 21:09
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    $\begingroup$ It might be wrong to say that Kyiv is likely attacked next because it has been attacked a lot in the past, but when we see some place being attacked very recently and predict that a next attack might occur in the same neighborhood, then the extrapolation is at a much shorter timescale. $\endgroup$
    – Sextus Empiricus
    Apr 14 at 21:12
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    $\begingroup$ @Tim yes I agree with all of your points here. The goal is not a complete historical analysis of the attacks. I am actually working on a model for civilian evacations. So given an attack today, what is the probability of attack in the surrounding neighborhood over the next 1 hour, 2 hours, 1 day, 3 days, etc. I need to estimate those parameters so that I can route vehicles around that area for the risky period. $\endgroup$
    – krishnab
    Apr 14 at 21:16
  • $\begingroup$ @SextusEmpiricus I agree. In the usual George Box fashion, "All models are wrong, but some are useful". Perhaps a model can be found that is useful. $\endgroup$
    – Galen
    Apr 14 at 21:18
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Does anyone know what kind of model I would use for something like this?
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I was just wondering if anyone know some common approaches.

Two approaches you may want to look into:

  1. "Self exciting Poisson processes" and similar. Quite a bit of literature comes up on a quick Google/Scholar search.
  2. "Species range distribution models." This drops your time series framework, but you might find it interesting to associate geospatial features with the attacks, as done in Elith, Jane, et al. "A statistical explanation of MaxEnt for ecologists." Diversity and distributions 17.1 (2011): 43-57.
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    $\begingroup$ thanks for the suggestion. I had not heard of the species range distribution models before, so that is interesting. I will take a look at those as well as the point process models. $\endgroup$
    – krishnab
    Apr 14 at 18:30

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