Statisticians Uncover the Mathematics of a Serial Killer

Hugh Pickens writes writes "Andrei Chikatilo, 'The Butcher of Rostov,' was one of the most prolific serial killers in modern history committing at least 52 murders between 1978 and 1990 before he was caught, tried, and executed. The pattern of his murders, though, was irregular with long periods of no activity, interrupted by several murders within a short period of time. Hoping to gain insight into serial killings to prevent similar murders, Mikhail Simkin and Vwani Roychowdhury at UCLA built a mathematical model of the time pattern of the activity of Chikatilo and found the distribution of the intervals between murders follows a power law with the exponent of 1.4. The basis of their analysis is the hypothesis that 'similar to epileptic seizures, the psychotic affects, causing a serial killer to commit murder, arise from simultaneous firing of large number of neurons in the brain.' In modeling the behavior the authors didn't find that 'the killer commits murder right at the moment when neural excitation reaches a certain threshold. He needs time to plan and prepare his crime' so they built delay into their model. The killings eventually have a sedative effect, pushing the neuronal activity below the 'killing threshold' – which is why there are large intervals of time between groups of murders. 'There is at least qualitative agreement between theory and observation [PDF],' conclude the authors. 'Stats can't tell you who the perp is, but they're getting better and better at figuring out where and when the next crime might happen,' writes criminal lawyer Nathaniel Burney adding that 'catching a serial killer by focusing resources based on when and where he's likely to strike next is a hell of a lot better than relying on the junk science of behavioral profiling.'"

Comments

They have 1 data point

[Anonymous Coward]

Aren't they jumping the gun a bit?

always some correlation to a single set of data

[Chrisq]

If you look hard enough you can always find some function that correlates to a single set of data. Like the analogy in a beautiful mind, you can find any pattern or picture in the stars if you look hard enough.

Re:always some correlation to a single set of data

[NoMaster]

True. The power law, though, is a particularly dangerous and entrancing trap to fall in to. Almost everything in nature - from pure randomness to highly structured effects - can be fitted to a power law. You often don't even need to do any transformation of the data - simply choosing the wrong set of dependent and independent variables to examine can do it.

My favourite goto whenever this subject comes up is the essay "So You Think You Have a Power Law - Well Isn't That Special?"

That said, I haven't read the current paper. They might have been very careful to avoid the common traps. I won't know until I spend some time tomorrow reading it.

"junk science" of behavioral profiling

[turing_m]

For behavioral profiling being a "junk science" they've had a lot of successes, and more success than this idea will ever yield (especially since it's so easily reverse engineerable, not to mention vague in its predictions). And the criticism coming from a criminal lawyer - well, I think the lady doth protest too much.

The basic idea of profiling is to narrow a large search down into a smaller one. The basis of the idea that by studying known offenders and finding commonalities between them, you'll have a clue as to the sort of person a perpetrator will be given an arbitrary new crime. Now that enough information about profiling is out there, offenders can and do reverse engineer the profiling process to make it tougher for them to get caught (assuming they are smart enough to do so - many are not that smart). However, at the very least there will be certain things that they are compelled to do otherwise the crime is simply not interesting for them to do. And certain things they have to do to carry out their crimes which will give a clue as to who they are.

The way I look at it, the people who study these particular criminals and offer advice for catching them are analogous to specialist doctors. For example, if you are trying to diagnose and treat some specialist skin condition that is very rare, you will have better results with a referral to a dermatologist than having the GP struggle and try to treat it as best he can.

Re:"junk science" of behavioral profiling

[nyctopterus]

Actually, profiling has been seriously challenged, there's a nice New Yorker article about it, and several scholarly papers, Alison L and Rainbow L. eds (2011) 'Professionalizing Offender Profiling: Forensic and Investigative Psychology in Practice'. Routledge, London. The charge is that profiling is similar to astrology, make vague claims that could match a variety of scenarios, and pay attention when it fits, not when it doesn't.

Like a lot of forensic techniques, it seems to have jumped from the theoretically plausible to practice, without going through the intermediate step of check that it works. "Junk science" may be a fair characterisation.