Charlie explains how he narrows down a suspect pool using reverse decision theory. He compares decision theory to a hunter. You can use decision theory to see what animal a hunter is most likely to kill. You can also use the reverse and look at a kill and determine which hunter was most likely to have hunted that animal.
While hunting for a criminal who is good at hiding his face, Don asks Charlie to see which crime syndicates their suspect may be a part of. To figure it out, Charlie explains the belief propogation which takes scattered data and pulls it into a coherent image.
In this scene, Charlie and Don realize that their mathematical model is wrong because they were focusing on the wrong factor (the home) as opposed to the right one (the criminal's workplace).
Charlie, Amita, and Larry explain how they can match a crime to a specific criminal using a quadratic discriminant analysis to see which known criminals are most drawn to a specific crime.