## May 17, 2007

### The "prosecutor's fallacy" in the Netherlands

A New York Times blog by Mark Buchanan on "The Prosecutor's Fallacy" provides a report on a conviction involving flawed statistical evidence. (The author also described the case in January in Nature. A more detailed analysis is at Richard Gill's website.)

Dutch nurse Lucia Isabella Quirina de Berk is serving a life sentence for seven murders and three attempted murders. Mr. Buchanan writes that:

Following a tip-off from hospital administrators, investigators looked into a series of “suspicious” deaths or near deaths in hospital wards where de Berk had worked from 1999 to 2001, and they found that Lucia had been physically present when many of them took place. A statistical expert calculated that the odds were only 1 in 342 million that it could have been mere coincidence.

After noting that the data collection was badly flawed and that "a more accurate number is something like 1 in 50," he adds that:

More seriously still – and here’s where the human mind really begins to struggle – the court, and pretty much everyone else involved in the case, appears to have committed a serious but subtle error of logic known as the prosecutor’s fallacy.

The big number reported to the court was an estimate (possibly greatly inflated) of the chance that so many suspicious events could have occured with Lucia present if she was in fact innocent. Mathematically speaking, however, this just isn’t at all the same as the chance that Lucia is innocent, given the evidence, which is what the court really wants to know.

Now, there are a great many instances of this fallacy of naively transposing P(E|H), the probability of the evidence E given the hypothesis H, into P(H|E), the probability of H given E. But surely this is not a more serious error than being off by a factor of some 10,000,000 in the estimate of P(E|H)! A p-value of 1/342,000,000 will be associated with a likelihood function that swamps any plausible prior probability distribution. See M.H. DeGroot, Doing What Comes Naturally: Interpreting a Tail Area as a Posterior Probability or a Likelihood Ratio, 68 J. Am. Stat. Ass'n 966 (1973).

Of course, Mr. Buchanan is right about one thing: the fallacy is subtle. He makes it when he describes the p-value as follows: "the odds were only 1 in 342 million that it could have been mere coincidence." The kind of statistics that appear to have been used in the case do not permit any quantitative statement about the probability that coincidence it the explanation for the nurse's presence. At best, they allow one to say that if that explanation is correct, it is exceedingly improbable that she would be present as often as (or even less often than) she was. Thus, if one wants avoid the transposition fallacy, one must say something like this: assuming the nurse's presence was mere coincidence, the probability of her being present at least as often as she was is only 1 in 342 million.

DHK

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In the serial murder case of Lucia de Berk statistics were used to link the two so-called murders, which were accepted by court and higher court as proven, to 7 deaths and 3 nearly deaths by natural causes, while she was present at these events.

With the acceptance of this technique of proof in court, the conclusion of natural deaths were changed into murders and Lucia was accused to be the actor of these events. G'd was innocent in these acts. This so-called chain proof in court is very remarkable. History shows where this type of reasoning leads mankind to.

The first case was a girl, who was supposedly killed by digoxin. In first instance prosecution found an average of (21 and 25) 23 microgram/liter in blood from gauze pads using Emit 2000 and IMX methods respectively and later 7 microgram/liter by the more precise method HPLC-ms in Strasbourg. The court however had chosen the 23 microgram as the best one, while the trials were known to be not specific enough to differentiate between digoxin and digoxin-like immuno-substances. The more precise 7 microgram/liter in Strasbourg and later reported was concealed by prosecution.

The history of these gauze pads, left behind in the belly is unknown. In the liver, kidney, brain tissue no concentration digoxin was found and for that reason not used in court! In Strasbourg the concentration happened to be 0 microgram/liter in liver, 4 in brains and 10 in kidney -- the conclusion in Strasbourg was: "probably contamination caused by gauze pads'.

But even more remarkable is that the contraction of the heart which occurs by digoxin-intoxication was not found in the autopsy, which shows without any doubt that murder by digoxin can't be the case. The second case was similar but with choralhydrate-intoxication, see .

All these facts were not used in Lucia's case. There was no shred of evidence which justifies any thought of murder. The used statistics to link these two cases to the 7 so-called murders and 3 attempts were in first instance 1 out of 4 or 7 billion, that she would be innocent.

An amateur-statistician dr. Elffers, in the meantime professor in court psychology, calculated 1 out of 342 million. Dr Richard Gill, professor in mathematical statistics and president of the Dutch Statistical Society, brought it back to one out of nine. Thus when you meet nine nurses you have a great chance, that a serial killer will be among them according to the Dutch court in The Hague. (Thus be warned when you take a trip to the Netherlands and visit The Hague as a judge in international law, one of the victims was a Japanese judge at the International Court of Justice.)

Gossip and rumors played a large role in Lucia's case. She was dressed differently, went to the nursing school at an older age, etc. This 'circumstantial evidence' was repeatedly used in the case to justify the ordeal by the 'character experts' about Lucia.

Lucia was presented as the Dutch serial killer by Paula Lampe in a book and would be as such presented by Lampe in a contribution to the international colloquium "Serial Murder and Criminal Assault in Hospitals: Investigation and Prevention" on the 19-20 march 2007 at the California State University Los Angeles. Richard Gill wanted to give a contribution to that colloquium about her complete innocent. The colloquium was canceled for unknown reason.

Internationally renowned scientist like US toxicologist Dasgupta ,
and UK statistician Dawid interviewed on NOVA TV, Sept 29 (11 minutes) speak of an horror story, see
More than 580 (71 professors) people have signed a petition to have the case reopened . These people with different academic skills see the Lucia's case as complete nonsense.

When the case is not reopened she has to stay the rest of her life imprisoned according to Dutch law. We are very worried about this emphatic lady Lucia de Berk, because she got due to stress during the trials a stroke and cannot anymore use her right arm and limps with her right leg.

There are many similar cases like Lucia's in the Netherlands. However Lucia's case is the worst of all.

Posted by: Metta de Noo / Nico Roosnek | Oct 23, 2007 7:09:35 PM