The ever excellent Numberphile have just released a really interesting video looking at what mathematical models are used to predict terrorist attacks and crime. Whereas a Poisson distribution assumes that events that happen are completely independent, it is actually the case that one (say) burglary in a neighbourhood means that another burglary is much more likely to happen shortly after. Therefore we need a new distribution to model this. The one that Hannah Fry talks about in the video is called the Hawkes process – which gets a little difficult. Nevertheless this is a nice video for showing the need to adapt models to represent real life data.