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## Statisticians Uncover the Mathematics of a Serial Killer164

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.'"
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## Statisticians Uncover the Mathematics of a Serial Killer

• #### Great. So now all we need... (Score:5, Insightful)

on Tuesday January 17, 2012 @03:15AM (#38722252)

...is another series of murders to consolidate the theory.

Any takers?

• #### Re: (Score:2)

by Anonymous Coward

Okay. I'll do it. It'll only be four people, though, is that enough? I hope so.

• #### Re:Great. So now all we need... (Score:5, Funny)

on Tuesday January 17, 2012 @05:01AM (#38722616)

I wonder if it also correlates to how often you post on Slashdot. We don't know who you are AC, but we know when you'll strike next.

• #### Re:Great. So now all we need... (Score:5, Interesting)

on Tuesday January 17, 2012 @07:58AM (#38723328)

Exactly. This whole hypothesis is based on one data point alone. There were more than one serial killers, why did they try their hypothesis on just this one? Or was he the only one who fit in the equation?

• #### Re: (Score:2)

They need more than just another series of murders... They need to have all the murders (I.E. bodies found after a delay will skew the data) and have them correctly attributed to the proper murderer (both missing and extraneous murders will skew the data). I.E. someone like Gary Ridgeway or Ted Bundy will likely either escape detection entirely or have wildly incorrect predictions. Not to mention killers like BTK who stopped entirely...

• #### Re:Great. So now all we need... (Score:4, Funny)

on Tuesday January 17, 2012 @10:16AM (#38724776) Journal
Someone's bound to take a stab at it sooner or later...
• #### Re: (Score:2)

And all he has to do is completely mess up the statistics and he could make a killing!

• #### so it was the mathamatician (Score:2)

in the library with the pencil
• #### They have 1 data point (Score:5, Insightful)

by Anonymous Coward on Tuesday January 17, 2012 @03:26AM (#38722300)

Aren't they jumping the gun a bit?

• #### always some correlation to a single set of data (Score:5, Insightful)

on Tuesday January 17, 2012 @03:45AM (#38722360)
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 [imdb.com], you can find any pattern or picture in the stars if you look hard enough.
• #### Re: (Score:2)

The question in science has always been, "does it have predictive power?"

• #### Re: (Score:2)

It can if you reapply the trick of staring hard enough at the experiment output until you see the desired result.

• #### Re:always some correlation to a single set of data (Score:5, Insightful)

on Tuesday January 17, 2012 @04:05AM (#38722428) Homepage Journal

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?" [umich.edu]

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.

• #### Re: (Score:2)

Agreed. I'd be very surprised if the data doesn't point just as strongly to an exponential distribution. Phrases like "the psychotic affects, causing a serial killer to commit murder, arise from simultaneous firing of large number of neurons in the brain" sound a little bit hand-wavey to me.
• #### Re: (Score:2)

A bit hand-wavey? You're being kind. Large groups of neurons collaborating to trigger a single event have been proposed to model precise timing, e.g. in movement, and locking behavior has been observed for speeds in the order of 100Hz to 5Hz, but synchronization over such a long period of time? And large groups? You would think that would be totally impossible. It sounds like
1. We don't know how a large group of neurons behave over long periods
2. We don't know what triggers a serial killer
3. ?
4. Publication

• #### Re: (Score:2)

That is what I am going to do, too - along with the umich.edu paper. I recently "found" a power law in some load- and performance testing data; I am suddenly growing suspicious of my own interpretation, which is always a Good Thing.
• #### Re: (Score:2)

Whether the distribution is precisely power law or exponential really doesn't really matter that much. With only 52 data points and anything more than trivial noise in the data, every model is going to be an approximation, right?

The bit of profound observation in the paper is surely that there is an aperiodic temporal pattern, and therefore a skewed distribution, that can be modelled with some accuracy. For one killer. And we all know, or should know, the dangers of generalizing from a single example.

• #### Re: (Score:2)

Thanks for that link. I subscribed to the "Three-Toed Sloth" feed.

I like the hopeful conclusion:
"I trust that I will no longer have to referee papers where people use GnuPlot to draw lines on log-log graphs, as though that meant something, and that in five to ten years even science journalists and editors of Wired will begin to get the message. "

• #### Re: (Score:3)

The oracle speaks. [umich.edu]
• #### Too little data, and not useful for prediction (Score:3, Informative)

on Tuesday January 17, 2012 @04:01AM (#38722410)

The 'murder probability' comes from a probability density function spanning three years, and is estimated from 53 data points, all from the same subject. That is hardly reliable.

And if we take the sparsity of the data for granted, what is the conclusion? That the less frequently the murderer acts, the less likely he is to act, and vice versa. It is a descriptive model, you can not predict the time of the next murder with it.

• #### Re: (Score:2)

What a fitting fortune cookie: Williams and Holland's Law: If enough data is collected, anything may be proven by statistical methods.
• #### Power law not usefully predictive in this case (Score:5, Insightful)

on Tuesday January 17, 2012 @04:05AM (#38722424)

I think the importance of what they found is overstated. The fact that a murderer's patterns fit a power law is not particularly helpful in really pinning down the time of the next murder. "The expected time of the next murder is a distribution of odds along this curve" is not particularly useful in trying to stop a single crime. Power laws are more useful predictors when applied across populations.

While unlikely to ever be predictive, this result is more interesting from a more academic perspective. It could help illuminate what might be going on in the brain of a serial murderer. Learning how damaged brains function (or fail to function) has long been a means of studying how non-damaged brains may work.

So this might provide some insight into how a compulsive thought builds up in the brain, but it's unlikely to ever allow a profiler to say "stake out this intersection on this night".

• #### Re: (Score:2)

That is true, but it could potentially be useful in linking murders to the same killer, in cases where the link otherwise might not have been made.

• #### Re: (Score:2)

This is exactly what I thought in this case. I immediately thought back to The Black Swan (Taleb's book, not the movie). There's a long discussion involving power laws. What most people don't realize about power laws is that a decimal of difference has quite a large effect. Besides, with comments about preventing these sort of things by allocating resources in advance to fit this power law you have to wonder if these authors understand the implications of sampling error. Even if this fits, it is a fairly
• #### This really isn't new to The Police (Score:3)

on Tuesday January 17, 2012 @04:17AM (#38722476)
• #### "junk science" of behavioral profiling (Score:5, Insightful)

on Tuesday January 17, 2012 @04:26AM (#38722500)

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 (Score:5, Insightful)

on Tuesday January 17, 2012 @05:27AM (#38722718) Homepage

Actually, profiling has been seriously challenged, there's a nice New Yorker article [newyorker.com] about it, and several scholarly papers [anu.edu.au], 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.

• #### Re: (Score:3)

Mod parent up. I don't know whether profiling works or not, but that final comment was certainly tacked on without justification.

1. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. Reasonable statement. ... P.
2. Th
• #### Re: (Score:3, Interesting)

The General Practitioner, however, does serve a purpose. He / She has general knowledge of a multitude of diseases, forming a kind of filter, that if he can't treat a disease, he can generally point you in the right direction (refer you to a specialist who may have better equipment / knowledge for a better diagnosis). If medical specialists are encyclopedic albums, then the General Practitioner typically serves the role of the index.

You don't want to be treated by a dermatologist if you need an oncologist.

A

• #### Re: (Score:3)

For behavioral profiling being a "junk science" they've had a lot of successes, and more success than this idea will ever yield

I agree. It sounds to me like the author has an axe to grind.

• #### Re: (Score:2)

Citation needed. The last estimate I read was something like a 5% success rate. I used that to make fun of Criminal Minds tv show, which has a near 100% success rate. That's the way profilers want to be seen, but it doesn't work out like that. So if you have numbers, preferably in percentages rather than total successes with no context, that would be a good start.

• #### Re: (Score:2)

Citation needed. The last estimate I read was something like a 5% success rate. I used that to make fun of Criminal Minds tv show, which has a near 100% success rate. That's the way profilers want to be seen, but it doesn't work out like that. So if you have numbers, preferably in percentages rather than total successes with no context, that would be a good start.

While I agree, CI doesn't have a 100% rate, but yeah a pretty darned unbelievable rate of like 99% or something. (They let one get away every now and again.)

• #### Chikatilo the subject of a movie back then (Score:2)

Was this the one protrayed by Malcolm McDowell? I don't know if anyone here has seen that... I think he was the only recognizable one in that film.

• #### Re: (Score:2)

Do you mean Citizen X [imdb.com] which starred Stephen Rea, Donald Sutherland, Max von Sydow?

• #### Just the data, ma'am, please.. (Score:5, Insightful)

<{gro.llehseerf} {ta} {sungam}> on Tuesday January 17, 2012 @04:44AM (#38722564) Homepage

Oh man, I get so bothered when someone presents interesting data - only to append a theory that isn't connected to it.
Why is that? Don't you get to publish unless you have a theory, no matter how unrelated an implausible it is?
Human sciences especially - it's understandable though, as it's hard to read people's minds.

Neurons firing? Really?? Does fantasizing about objects we can actually see and touch suddenly make it science?
If the study included brains scans or something, sure. But all they did was look at numbers.

If you don't have a theory that's related to your study, just post your data and spare us your fantasies. Thank you.

• #### Re: (Score:2)

If you don't have a theory that's related to your study, just post your data and spare us your fantasies.

Posting datasets and the theories that do NOT fit is also valid... though the publication should note that it's main purpose is to get the data out there and show that some work was done to "figure out" the data but no conclusions were drawn.

• #### Re: (Score:2)

It would be great if you kept to one point on a rant. Generally, adding a theory does bother me, because in a lot of cases it seems very convoluted, and in many cases does not even follow from the data presented.

You also seemed to attack the premise of neurons firing, suggesting it lacked credibility. I think this makes sense, in the same way as someone who takes anti-psychotic medication, then skips it for a while. In this case, killing takes the place of the medication, sating whatever imbalances or pr

• #### The Sudoku Killer (Score:5, Funny)

by Anonymous Coward on Tuesday January 17, 2012 @04:50AM (#38722586)

And in other news, police warn that the Sudoku killer will kill either 1, 4, or 9 victims next.

• #### Power-Law distributions in empirical data (Score:4, Informative)

on Tuesday January 17, 2012 @04:57AM (#38722608)

Here is the abstract of an article, "Power-Law distributions in empirical data" by Clauset et al (2009):

"Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events— and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a powerlaw distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out."

So, I would recheck this guy's analysis.

• #### That seems backwards (Score:2)

Given any dataset, you can come up with a formula that would match it.

That doesn't mean though that if they tried doing this back when he was on his 3rd or even 20th murder, they'd have managed to come up with something useful.

• #### North Korea (Score:3)

on Tuesday January 17, 2012 @08:01AM (#38723352)
Makes you wonder if this might be fertile ground for (non-government sanctioned) serial killers as well, given that people no doubt disappear all the time and no one is foolish enough to ask about them. Chikatilo might turn out to be a piker.
• #### 1 guy (Score:4)

on Tuesday January 17, 2012 @09:09AM (#38723878) Homepage

You don't build a statistical model off of a single person.

• #### Psychopaths (Score:3)

on Tuesday January 17, 2012 @09:32AM (#38724176) Journal

I don't know if Chikatilo was a psychopath, anyhow, psychopaths seem to enjoy hurting others and are usually pretty smart. There is a secure institution where a buch of psychopaths managed to get hold of the manual for a well known profiling instrument that, effectively scored psychopathology from 0 to 40. They then had t-shirts printed with just "Perfect 40" on them. Point being that once something is public knowledge the kinds of people who engage in this kind of activity are likely to pay attention and work to throw predictive algorithms off, simply because they would gain a great deal of satisfation doing so.

• #### How Many Deaths for a Sufficient Data Set? (Score:4)

on Tuesday January 17, 2012 @10:04AM (#38724640)
This is nice and all, but how many people need to be killed by a serial killer in order to get a sufficient data set to mathematically model his killing pattern?
• #### Re: (Score:2)

Well, isn't any number less than the number he would have killed had he been allowed to die of natural causes, by definition, an improvement?

The tool is what it is, if it is anything, of course. Leaving aside whether this may actually be meaningfull, the attempt here is to figure out how to apportion resources towards actually catching a serial killer. You have to consider it in that context. These crimes are happening, and will continue to happen, whether anything is done or not. There are limits to the re

• #### Citizen X (Score:2)

Incidentally, there was a pretty decent movie with Stephen Rea and Donald Sutherland about the hunt for Chikatilo called Citizen X [imdb.com].
• #### this too is profiling... (Score:4)

on Tuesday January 17, 2012 @02:14PM (#38728078) Journal

Sorry, but, hand-waving at neurons to justify the power law they found is none the less also....

"relying on the junk science of behavioral profiling"

There is one way to find out if a man is honest -- ask him. If he says "Yes" you know he is crooked. -- Groucho Marx

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