Estimating probability of attack in Ukraine, given count data 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.

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.
 A: 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.
A: 
Does anyone know what kind of model I would use for something like this?
...
I was just wondering if anyone know some common approaches.

Two approaches you may want to look into:

*

*"Self exciting Poisson processes" and similar. Quite a bit of
literature comes up on a quick Google/Scholar search.

*"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.

