Statisticians Uncover the Mathematics of a Serial Killer 164
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.'"
Too little data, and not useful for prediction (Score:3, Informative)
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.
Power-Law distributions in empirical data (Score:4, Informative)
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.
Re:Obvious problem? (Score:2, Informative)
I wonder how they got their hands on the brain activity data of a serial killer in action?
They didn't. They "assume" it may be the same as epilepsy based on a 1879 (yes, 1879) book by a criminologist called Lombroso who believe that crime was caused by hereditary defects or the 'reversed' evolution of some populations. While discredited by later work, it remained a favourite source for people who wanted reasons to believe certain populations were inherently criminal or defective, in order to justify exterminating or sterilising them (along with the disabled).
However, Lombroso [5] long ago pointed out a link between epilepsy and criminality. A link between epilepsy and psychosis had been also established [6]. Thus, one may speculate that similar processes in the brain may lead to both epileptic seizures and serial killings.
While I am not a very 'politically correct' person, I believe that scientific papers should avoid making grossly offensive comparisons (even as 'speculation') about disabled people unless they can produce solid evidence and references less than 130 years old.
They then develop a model of neurons firing that they already know analytically will produce a power law and do a numerical simulation to show it produces a power law.
They then plot the simulation against the data on a log-log graph and claim they are similar, although there is no actual statistical analysis in the paper. Also, to me they don't actually look that similar, other than both having heavy tails. This is the attempt to comment on the central claim of their thesis:
Figures 2-3 show the results of these simulations. They decently agree with the experimental data.
There is no attempt to consider other possible models such as exponential etc. There is no comparison with datasets from other serial killers.
Re:Yeah I saw that on... (Score:5, Informative)
Also, Superman doesn't really live in New York City,
We know that. He lives in Metropolis. Duh.