Lucia de Berk en de amateurstatistici (in Dutch)

May 31, 2007

Deze tekst, die geschreven werd in mei 2007 als een vertaling van de Engelstalige blog Lucia de Berk and the amateur statisticians, is vervangen door een recente blog (2009): Het Openbaar Ministerie contra de wetenschap in de Lucia de Berk zaak. Het OM heeft nu inmiddels openlijk toegegeven anti-wetenschappelijk te werk te willen gaan door een “forensisch criminalistische benadering” te willen stellen tegenover een “wetenschappelijk theoretische benadering”. Voor meer details, zie Het Openbaar Ministerie contra de wetenschap in de Lucia de Berk zaak


Lucia de Berk and the amateur statisticians

May 28, 2007

My father was a judge. The only reason for bringing this up is that the cheapest argument, which has been used to fight people who have an opinion on the Lucia de Berk case which runs against the court decisions, is to say that they have no understanding of how the Dutch law system works. This “argument” has even recently been used by the “statistician of the court” Henk Elffers. It is similar to the argument, used against people expressing a negative opinion on “Apartheid” in South Africa at its prime time: “You must have been there to make a judgment”. So if it is going to be like this, I can only say that I have a lot of first hand experience with Dutch Law and Dutch lawyers.

I have been following the Lucia de Berk case for several years now. Among other things, I attended, on April 2, 2004, a discussion afternoon of the Dutch Statistical Society at the “Vrije Universiteit” in Amsterdam. The statistics professor Aad van der Vaart was chairman of that meeting, and among the discussants was Henk Elffers. In the intermission I had a short conversation with him. Henk Elffers and I knew each other from the time that we were at the Mathematical Centre, Amsterdam. Although part of our conversation was on music, I also asked him whether there was some “hard” evidence for Lucia’s guilt. Then he mentioned the traces of intoxication found in the blood of the victims, which at that time still sounded rather convincing. In view of this, his computation of the very small probability of the “coincidences” in the Lucia de Berk case, which had not convinced me at all, sounded like an academic exercise without much consequence. However, at present I think that this computation is one of the terrible errors in a whole chain of unfortunate errors that have led to the conviction of Lucia de Berk.

How did all this start? One of the initiators was Mr. Smits, general director of the Juliana children’s hospital and the Red Cross hospital in the Hague, the first amateur statistician on the scene. As a good manager, he had access to the Microsoft Excel spreadsheet tool, containing a button called “random”. Using this, on the (retrospectively) historical day of September 4, 2001, he (or one of his employees, this is not entirely clear) made a quick computation of the probability that Lucia de Berk had been present with so many “incidents” (as had been “observed” by other nurses). And by this quick computation he became convinced that so many incidents “could not be a coincidence”. Twelve days later the police was contacted and Lucia de Berk was accused of 5 murders and 5 attempted murders in the Juliana children’s hospital. In the mean time Mr. Smits had also looked into the possibility of additional murders by Lucia de Berk in other hospitals and yes, more potential murders were quickly found. As expressed in the book of Ton Derksen on the Lucia de Berk case (“Lucia de B. Reconstruction of a Miscarriage of Justice”, in Dutch): “We have the suspect. Could you please find for us the murders she committed?”. And yes again, on September 17, 2001, Mr. Smits can report to the police 4 additional suspicious deaths in his other hospital, the Red Cross hospital.

On top of all this, the boards of Mr. Smits’ hospitals contacted the morning newspaper “De Telegraaf” (having a high profile on sensation news, in this respect somewhat comparable to the British “The Sun”). This newspaper issued on September 17, 2001, an item on the case, which in fact stated that a nurse in the two hospitals had possibly been involved in the killing of several adults and children. The newspaper item also said that the directors of the hospitals regretted very much what had happened and that they expressed their sympathy with the parents (after expressing their concern that the trust of patients in their hospitals might be somewhat shaken by this message). Note that this suggested that at this point the “murders” had already been proved “beyond reasonable doubt” (I note in passing that the Dutch law system does not make use of this concept, I am sorry to say). And if all this were still not enough, a spokes(wo)man of the office of the Prosecution made it known (in the same news item of “De Telegraaf”) that “the possibility of more cases” (of killing or attempted killing by Lucia de Berk) “was not excluded”. All this 13 days after the Microsoft Excel spreadsheet calculation!

Ironically, another spreadsheet table of director Smits (exhibited on p. 22 of the second edition of Derksen’s book) shows that in the years that Lucia de Berk was not employed by the Juliana children’s hospital there were in fact more deaths than during the time that Lucia de Berk was employed by the hospital, whereas one would be inclined to expect that the opposite would hold if a serial killer were around in this hospital. Moreover, all the suspicious death cases of which Lucia was accused had been declared “natural” and now had to be redeclared as “unnatural” by the hospital. But anyway, after all this heat an unstoppable chain reaction started, Henk Elffers did his nonsensical computation and the court in The Hague had enough to start the prosecution.

Long ago, while still a student, I gave, in cooperation with Willem Albert Wagenaar and Gerard de Zeeuw, a course called “The intuitive statistician”. This course was investigating what people understand of “randomness”, for example by presenting them with sequences produced by a random number generator (and also with sequences with some very strong embedded structure). Many experiments have shown that people have the tendency to expect random sequences of coin flippings to have much faster alternation of heads and tails than in in fact happens in random sequences of independent flippings. And indeed, the attendants of our course were also prone to this fallacy. This particular fallacy is called the “gambler’s fallacy”. I think that Mr. Smits’ unfounded calculation arose from a similar type of faulty intuition.

This brings up a more general point. In such an important case as the case of Lucia de Berk, where even the Dutch supreme court was involved, the court could have consulted a professor of mathematical statistics in the Netherlands. The court could have consulted, for example, professor Aad van der Vaart in Amsterdam, professor Sara van de Geer in Leiden (at that time, now she is professor of statistics in Zurich), professor Richard Gill in Utrecht (at present professor of mathematical statistics in Leiden) and also myself in Delft. Why didn’t the court do that? Why were they relying on amateur statisticians all the time?

How would the judges feel if, at the “moment suprême”, just before being rolled into the surgery room for a brain operation and perhaps wondering why the anesthesiologist did not already send them into unconsciousness, the nurse would casually mention that the operation would be performed by an amateur surgeon?

First there was amateur statistician Mr. Smits. After that there was, I am sorry to say, amateur statistician Henk Elffers. On the personal level I have absolutely nothing against Henk. But I think that he made a formal and totally pointless calculation, using the Fisher exact test for a 2×2 table, about the only thing he learned from his professor of mathematical statistics in Amsterdam (see below). As I mentioned above, Henk Elffers and I were at the Mathematical Centre at the same time (although I stayed a little bit longer, after finishing my dissertation). At the time that Richard Gill and I were writing our dissertations at the Mathematical Centre, Henk did not write a dissertation, and in fact went on to start another study, and to do completely different things (a summary of his career is in fact given on the Home Page of Henk Elffers). That’s in itself fine of course, but it means that he lost contact with what is going on in mathematical statistics. Mathematical statistics is not about balls and boxes. Mathematical statistics is about the choice of an appropriate model. In that sense mathematical statistics is also fundamentally different from Probability Theory, and certainly from discrete Probability Theory, working with balls and boxes. Probability Theory works with one model of which it explores all the consequences. Mathematical statistics usually deals with a continuum of models of which it tries to pick the most appropriate one. One can wrestle through 100 pages of boxes and balls without understanding anything of what mathematical statistics is about.

Unfortunately Henk Elffers had his training from a professor of mathematical statistics who spent almost all his teaching time on balls and boxes (erroneously assuming that this was needed before going on to the real thing). I know, because I followed courses of the same professor of mathematical statistics, whom I actually succeeded at the University of Amsterdam in 1984. He was also our boss at the Mathematical Centre. I think that Henk Elffers’ understanding of mathematical statistics has not gone very far beyond this understanding of the behavior of balls in boxes. Moreover, even his understanding of these basic facts had apparently eroded somewhat during all these years he was doing other things, since he made some elementary errors in his computation, as shown in Elffers corrected. For example, he assumed that the product of (so-called) p-values is again a p-value. The absurd consequence of this type of error is that a nurse who has worked in several different hospitals has a higher chance of being accused of murders than a nurse who only has worked in one hospital at the same time, although the number of “suspicious coincidences” might be exactly the same for the two nurses.

Furthermore, it is a mistake to think that these balls in boxes provide “objectivity”. There is only the illusion of science and objectivity, nothing more. The (in my view) most satisfactory computation in the Lucia de Berk case, which still has to be further expanded, is given in: Elementary Statistics on Trial. This indeed works with a continuous (that means, among other things: an infinite) family of models, and arrives at a probability of 1 in 25 that a nurse can be confronted with a series of coincidences as in the Lucia de Berk case (calculations, based on earlier available data even gave a probability of 1 in 9; since the hospital defines what an incident is, and since “natural deaths” were later declared to be “unnatural deaths” if Lucia de Berk happened to be on duty, the data on which one has to base these calculations cannot be trusted anyway). Compare this to the amateur calculations of Mr. Smits and Henk Elffers. Henk Elffers gets probabilities of the order of 1 out of 342 million! Mathematical statistics is a rather subtle discipline in which one has to be very careful! It is not for amateurs!

Still another amateur statistician, consulted by the court is (Prof. Mr.) Richard de Mulder, who studied Law and Business Administration. One would like to know why the court chose him as an expert on statistics. Was it because he confirmed the computations of the other amateurs, Smits and Elffers? Again, why didn’t the court consult a real professor of mathematical statistics?

Until recently I was under the impression that Prof. Mr. de Mulder was chosen as independent expert, who was asked to verify the computation of the “law psychologist” Henk Elffers. But I recently learned that the situation is even more grim and that the court did not even try to get an independent expert or a second opinion: Prof. Mr. de Mulder’s task was to explain Elffers’ computation to the court. Apparently, the court did not understand his computation. Joint publications of Henk Elffers and Richard de Mulder date at least back to 1999, as can be verified on the page Richard de Mulder. If I am rightly informed, the court asked Prof. Mr. de Mulder because he is a lawyer, and because the claim of the court was that an explanation of a real statistician would be incomprehensible. But I think that the latter claim has no basis, since they simply never tried to consult a real statistician.

In the final court verdict (also issued to the press) it is stated that statistics did not play a role in the final verdict. This is only true in the sense that the court did not consult even one professor of mathematical statistics in the Netherlands. On the other hand, Ton Derksen’s book makes it very clear that faulty and amateur “statistical” arguments are in fact the only thing the court has. All cases which first were brought forward as “hard evidence”, based on the digoxin intoxication, etc. have in the mean time dissolved into thin air. As an example, the anxiously waited for report from Strasbourg on the supposed digoxin intoxication of the liver of the child “Amber” did not confirm this intoxication at all (and has remained in a drawer for two years for still unexplained reasons). Medical expert witnesses who expressed the opinion that the suspicious deaths could very well be natural deaths have not seen their declarations on these matters make it into the final report of the court. So in the end a silly quasi-statistical computation on coincidences is the only thing that remains. For further news and discussion, see: The Lucia de Berk case, part 2. The petition for reopening the Lucia de Berk case can still be signed, see: Petition for reopening the Lucia de Berk case.


Ian McEwan and the bouquet series

May 8, 2007

Once upon a time… I knew a girl who would buy at the supermarket, together with the usual things one buys in a supermarket, a new small volume of the so-called “bouquet series”. She considered this to be a weakness or perhaps a “compulsion” (a rather innocent compulsion, perhaps similar to the compulsion of Lucia de Berk to spread Tarot cards). These small volumes could be classified into several categories; for example there were the “castle novels” (I realize that the word “novel” might be a bit heavy in this context, but it’ll have to do for the moment) and “doctor novels”. On the first page of novels of the latter type a successful good-looking (usually male) doctor would be introduced and some kind of romance would start to develop with a nurse or female colleague (I recently learned that the French equivalent for a novel in the Dutch bouquet series is a “roman de quai de gare” or “roman à l’eau de rose”).
I was reminded of this when reading the first line of Ian McEwan’s book “Saturday”, recommended by the Observer as “Dazzling… profound and urgent”:

“Some hours before dawn Henry Perowne, a neurosurgeon,…”

Let’s compare this with the first sentence of “The catcher in the rye” by J.D. Salinger:

“If you really want to hear about it, the first thing you’ll probably want to know is where I was born, and what my lousy childhood was like, and how my parents were occupied and all before they had me, and all that David Copperfield kind of crap, but I don’t feel like going into it, if you want to know the truth.”

If we believe that the first page of a book “sets the tone”, it is clear that the first page of Ian McEwan’s book “Saturday” sets a rather different tone than the first page of Salinger’s catcher in the rye. And indeed, after the introduction of the neurosurgeon Henry Perowne, we get some information on the really nice house he is living in, we get to know his wife Rosalind who is a highly successful lawyer (“She’s due in the High Court at ten for an emergency hearing”, p. 24) and his son Theo.

Ouch! His son Theo didn’t do to too well at school and won’t read books! But not to worry: Theo is a highly successful blues musician! Moreover, to compensate for the illiteracy of Theo, there is his sister Daisy (both “sensuous” and “intellectual”!): “His little girl, slipping away from him into Parisien womanhood, is expecting her first volume of poems to be published in May.” (p. 49).

Moreover, in a shrewd combination of the doctor novel and the castle novel, there is granddad -what’s in a name- Grammaticus in his castle (“chateau”) in France, inherited from the parents of his wife. Yes, we almost have to say aloud, following Henry Perowne on p. 55: “There is grandeur in this view of life.”!

After all this one is almost craving for the first loser to enter the scene. And, be assured… there will be such person! This character, named Baxter, certainly is as “loserish” and “havenottish” (to coin two new words) as can be. But one feels that in reality his main function there is to demonstrate the superiority of the family Perowne (+ granddad Grammaticus, owner of the French castle and father of Henry’s wife). In the decisive scene of the novel, daughter/poet Daisy reads a poem to Baxter, just when he is on the verge of afflicting the family physical harm or worse. This, however, after -as a special treat to the bouquet series readers- Daisy had to undress herself (which reveals that she is pregnant) in front of her parents (“Perowne hasn’t seen his daughter naked in more than twelve years”), granddad Grammaticus, her brother Theo, Baxter and his second man Nigel, as requested by bad, bad, but, at the same time, miserable Baxter.

Then Baxter falls to the spell of the poem and everything ends well. “End well, all well”, as fairy tales often end (in Dutch), although we have to admit that Baxter’s end will not fall into this category.

Now, just to know whether this bouquet series thing was a systematic feature of McEwan’s writing, I also read his most recent novel “On Chesil Beach”. And yes, it seems to be systematic… Another time I might say more about this last novel and discuss my views on general laws of composition with it. I guess I would also have to read the novel for which he got the Booker prize, called “Amsterdam”, although I am not particularly looking forward to that.

But I want to touch now on a more general issue, which concerns development of style during the past century. One reads McEwan’s novels and it seems that, for example, Salinger has not been there. And all these French authors of the past century, Nathalie Sarraute, Louis-Ferdinand Céline, Robert Pinget, Raymond Queneau, to name just four. Long ago Paul Valéry said something like: “I will never be able to write a novel, because I never could write: “Countess X opened the door for count Y and said….” (I have to warn you that I am trying to reproduce the gist of what he was saying, and this is certainly not a literal citation!). Exactly for that reason, I believe, Nathalie Sarraute has people without names or (specified) occupations in a lot of her books. We just fall into the middle of a conversation (as in “Martereau”, “Les fruits d’or” or the great play “Pour un oui ou pour un non”). But, in spite of this lack of information, we know immediately what is going on.

And with respect to the question whether one should have “winners” or “losers” as main characters of a novel: of course these categories do not really mean very much, although they are popular themes in American movies. But just to stick to Salinger’s book: it has advantages to introduce as a main character someone who is not too successful. Why? Because it frees the mind for things that really matter! The “I” of “The catcher in the rye” (called “Holden Caulfield”) has been kicked out of school, doesn’t do well in any subject, except perhaps English, but certainly has the “power of observation” (which is of course the author’s power of observation). I’ll just cite a whole passage here to illustrate my point.

“It wasn’t as cold as the day before, but the sun still wasn’t out, and it wasn’t too nice for walking. But there was one nice thing. This family that you could tell just came out of some church were walking right in front of me – a father, a mother, and a little kid about six years old. They looked sort of poor. The father had one of these pearl-gray hats that poor guys wear a lot when they want to look sharp. He and his wife were just walking along, talking, not paying attention to their kid. The kid was swell. He was walking in the street, instead of on the sidewalk, but right next to the curb. He was making out like he was walking a very straight line, the way kids do, and the whole time he kept singing and humming. I got up closer so I could hear what he was singing. He was singing that song, ‘if a body catch a body coming through the rye.’ He had a pretty little voice too. He was just singing for the hell of it, you could tell. The cars zoomed by, brakes screeched all over the place, his parents paid no attention to him, and he kept walking next to the curb and singing ‘If a body catch a body coming through the rye.’ It made me feel better. It made me feel not so depressed any more.”

Salinger also has a striking description of how he might want to express his appreciation or lack of it to an author of the book he just read. I’ll quote some relevant passages here. “What I like best is a book that’s at least funny once in a while”. How does this apply to “Saturday” and “On Chesil Beach”? Mmm… These books might be “Dazzling… profound and urgent”, to quote the Observer again, but “funny once in a while” is not the first thing that comes to mind. A friend of mine has the theory that it is McEwan’s intention to make a caricature and that, in “Saturday”, he wants to illustrate the “emptiness” of the life of middle-upper class families, living in London. An interesting theory (in which I personally do not believe)! If this really were his intention, then the book should be “at least funny once in a while”.

Holden Caulfield continues to say in “The catcher in the rye”: “What really knocks me out is a book that, when you’re all done reading it, you wish the author that wrote it was a terrific friend of yours and you could call him up on the phone whenever you felt like it. That doesn’t happen much, though.”…