Details

The formula used to find the probability of the criminal's residence is

,

where the sum is over crime locations and

.

Here is a point in the grid and is the distance to a crime location with a choosen metric, either the Manhattan or Euclidean distance. The "buffer zone" is the area where the criminal does not commit crimes; is its radius. The powers and affect the decay of the curve.

[1] J. Kun. "Hunting Serial Killers." (Jul 20, 2011) jeremykun.com/2011/07/20/serial-killers.

[2] R. A. Martin, D. K. Rossmo, and N. Hammerschlag, "Hunting Patterns and Geographic Profiling of White Shark Predation," Journal of Zoology, 279(2), 2009 pp. 111–118. doi: 10.1111/j.1469-7998.2009.00586.x

[3] SuperJustimagine. Geo-profiling on Numb3rs [Video]. (Aug 15, 2010) www.youtube.com/watch?v=AUub-ch_ULM.

[4] "The Math behind Numb3rs: Pilot Episode." (2007) numb3rs.wolfram.com/season1.html.