Posts Tagged ‘serial killer’

Statistics and the Serial Killer

Monday, January 16th, 2012

Andrei Chikatilo was serial killer who murdered at least 56 young women and children starting in 1978 until his capture in 1990. The details are as bad as one might expect, and apparently the murders and mutilations were how he achieved sexual release. His killings seemed unpredictable to investigators at the time, and even in retrospect there appears to be no clear pattern.

Now, however, UCLA mathematicians Mikhail Simkin and Vwani Roychowdhury have published a paper where they see not only a pattern, but one that is meaningful to those who might want to stop other serial killers. In their paper, “Stochastic Modeling of a Serial Killer,” published a couple of days ago, Simkin and Roychowdhury discovered that the killings fit a pattern known as a “power law distribution.” One of many kinds of statistical distribution (the bell curve being another), power law distributions are often found for out-of-the-ordinary events like earthquakes, great wealth, website popularity and the like.

First, they looked at a timeline of his killings. They saw apparently random periods of inactivity. Each time Chikatilo started killing again, however, the next murder would come soon after. And the one after that even sooner. And so on and so on until the next period of no killing.

The study doesn’t take account of the reasons for two of the longer pauses — Chikatilo’s first arrest and detention on suspicion of being the killer, and the period where the media started reporting on the investigation — but the reasons aren’t important. What’s important is being able to make some kind of sense out of the seemingly random events.

What they noticed was that, when these ever-increasing murders were plotted on a logarithmic scale, they came out in almost a straight line — indicating the possibility that a power law might be at work here. What’s more than that, they noticed that the curve’s exponent of 1.4 was pretty darn close to the 1.5 found for the power curve of epileptic seizures. What if (they wondered) the killings fit a neurological pattern? What if, like epileptic seizures, psychotic events like these killings came about when an unusually large number of neurons in the brain started firing together?

So they plugged in some givens of what is known about how neurons work, modeled on how epilepsy works. They made the model a little more realistic — seizures come unbidden when the conditions are met, but killers probably need some time to plan once their brain is ready for the next attack. Then they ran a simulation.

The simulated probabilities for the length of time between murders tracked the real-life data almost perfectly.

In other words, if you know when the last murder took place, you can calculate the probability that another killing will happen today. And the more time has passed since the last one, the less likely another will happen.

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Fascinating stuff, but so what? The so what is that (more…)