The Lucia de Berk case, part 2

Making errors is so common in mathematics that there is not too much embarrassment about it. For example, both Cauchy (1789-1857) and Kummer (1810-1893) made a very serious error in attempting to prove the Fermat conjecture, which was finally proved by Andrew Wiles at the end of the previous century, using tools Cauchy and Kummer could not have dreamed of. Cauchy (a really very famous mathematician, whose name pervades mathematics in all kinds of results) had to withdraw a paper he had submitted to the French Academy of Sciences which claimed to prove Fermat’s conjecture. Kummer made a similar error, but after the mistake was pointed out to him by the mathematician (and successor of Gauss in Göttingen) Dirichlet, he set out on a completely new track. E.T. Bell (see p. 522 of: “Men of Mathematics, volume 2″, Pelican Books) says about this event: “This failure of Kummer’s was one of the most fortunate things that ever happened in mathematics. Like Abel’s initial mistake in the matter of the general quintic, Kummer’s turned him into the right track, and he invented his “ideal numbers””. Abel (1802-1829), another outstanding mathematician…

The book by Ton Derksen, “Lucia de B. Reconstruction of a Miscarriage of Justice” (in Dutch), discussed the errors made by the prosecutors, judges and consulted experts in the case of Lucia de Berk. Like the mistakes of Cauchy, Kummer and Abel, admitting these mistakes might conceivably set the people in the Dutch legal system who are involved in this case onto the right track. It did not happen… Instead, there seems to be a culture of denial of mistakes made. Outside the rather closed group of Dutch lawyers consisting of prosecutors, judges, etc. (including the Supreme Court), scientists and other non-lawyers fear that because of all recent cases of judicial errors in the Netherlands (the most conspicuous one is the so-called “Schiedam Park murder”, see Miscarriage of justice, where the judicial errors came to the surface just because someone other than the convicted person confessed having committed the crime, and not because of efforts of persons inside the Dutch system of law; the Court in the Hague still claims not to have committed any errors!), the people involved in the Dutch legal system will refuse to reopen cases where there is a serious suspicion of miscarriages of justice. Just for fear of more embarrassment and for getting publicly a bad (or worse) name.

As I mentioned in my blog Lucia de Berk and the amateur statisticians, 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. And, since I stated that the “statisticians” consulted by the court were amateurs or acting as such, the corresponding cheap reply of persons defending this Court verdict is to say that I am an amateur lawyer and should therefore keep my mouth shut about law cases. And the same reproach has been addressed to Richard Gill who spends a large part of his time nowadays in fighting for justice in a number of cases where he (and also I) suspect that serious miscarriages of justice in the Netherlands have happened.

But there is an essential difference between my reproach of the amateur statisticians not doing a proper job and the “counter reproach” that I am an amateur lawyer and should therefore keep my mouth shut. The amateur statisticians come forward with statistical statements. These statements should be evaluated by statisticians. Richard Gill and I do not comment on law or make statements of a judicial nature. Our observations are external to the legal system itself, in that they do not concern the system but rather the way this appears to be (mis)used or (mis)applied. Any person in society, not just lawyers, can and may make such statements. The same cannot be said of doing statistical computations, though.

Of course everyone can try to do amateur statistical computations, like Mr. Smits, general director of the Juliana children’s hospital and the Red Cross hospital in the Hague, the law psychologist prof. Elffers, or Prof. Mr. de Mulder in his role of explaining to the Court the computations of his colleague prof. Elffers, but these calculations are open to criticism from statisticians. And this is indeed what happened: the flaws in these calculations have been exposed in, for example, Elffers corrected. People in the Netherlands have been using the Dutch expression “Tailor stick to your trade!” in saying that Richard Gill should not have pointed out the implications of these errors for the Lucia de Berk Court case. What kind of repressive mentality is this? In fact, Richard Gill was sticking to his trade by correcting the calculation! The next step was to point out the implications of this for the Court case. Is this next step not allowed? Should he just have let it pass, waiting for the people involved in the Dutch legal system to do something with this information? I personally think that he would have waited forever.

The the Hague Court verdict in the Lucia de Berk case (after appeal) is publicly available. I have made the print version of this verdict available in: the Hague Court verdict (in Dutch). On page 1 of the print version we read the statement (I translate literally): “Statistical evidence in the form of probability calculations has not been used”. What is the meaning of this statement? Amateur statistics have played a role in every phase of the Court case, as I will now explain more fully.
1. Henk Elffers convinced the police that “so many incidents could not be a coincidence”.
2. He secondly convinced the (two) Courts (second one after appeal) that “so many incidents could not be a coincidence”. As possible alternative explanations (besides murder) for “so many coincidences” he offered 5 explanations on page 7 of his first NSCR report (in Dutch), by way of example (Henk Elffers has to be praised for making this publicly avalaible). He also stated that an explanation should be given for “so many coincidences”.
3. Prof. Mr. de Mulder in his role of “expert in statistics” has stated that “Yes, Elffers’ computation is correct, and yes, an explanation for the coincidences has to be found”. The Court has interpreted this as: our suspect Lucia de Berk should provide the explanation.

The Court has presented Lucia de Berk with 3 of the 5 alternative explanations of the “coincidences” on page 7 of first NSCR report Elffers. The following two other explanations were not applicable or not applied:
a) Lucia de Berk preferred to work with another nurse who caused the incidents.
b) Someone tried to “frame” Lucia de Berk.
Explanation a) was not applicable and explanation b) was not applied, and, in any case, Lucia de Berk was not in a position to comment on the truth or falseness of this explanation.
The three other explanations on p. 7 of Elffers’ report were:
c) Lucia de Berk (denoted by “V” in Elffers’ report) often did night shifts and there is a higher chance during the night that a life-threatening situation is not discovered in time.
d) Lucia de Berk is a bad nurse and does not spot dangerous situations in time.
e) Lucia de Berk always takes the most difficult cases.

One can read the use of this in the the Hague Court verdict, (see p. 77 and pages thereafter, if one can read Dutch). As an example, p. 79 of the verdict says:
“One cannot consider as a plausible explanation that the suspect is not a good nurse, where one’s attention should in particular be on her functioning in the Juliana Children’s hospital. Suspect has declared in the Court session, March 22, 2004: “I think that I have been a good nurse. I cannot think of anything which I often did wrong or should have done differently and where there is a causal connection between one or more incidents. It is correct that I have declared in an earlier Court session that I consider myself to be a good nurse.””
This does away with explanation d). And explanations c) and e) are discarded by the Court in a similar way. This leads the Court to say, see 11.13, p. 78: “No plausible explanation has been found for the fact that suspect was present with so many deaths and life-threatening incidents in such a short period”.
Well, the Court now argues (somewhat implicitly perhaps): “The five alternative explanations in Elffers’ report do not apply. Then only one possibility remains for the coincidences: Lucia de Berk must be a murderer”. In the pages preceding p. 77 it is argued that there were two cases where there was “hard evidence” (for example, digoxin intoxication). This “hard evidence” has dissolved into thin air, as discussed in my blog Lucia de Berk and the amateur statisticians and further detailed in the book by Ton Derksen, see also Lucia de Berk.

So it is clear to everyone who takes the trouble of reading the 90 pages of the the Hague Court verdict that, quite contrary to what the opening remark “Statistical evidence in the form of probability calculations has not been used” (also issued to the Dutch newspapers) suggests, (bad use of) statistics is everywhere in the verdict.

There is still something else. Everybody is free to make a statement about a mathematical problem. Mathematicians will never say: you should keep your mouth shut because you cannot show that you have a certificate showing that you finished a study in mathematics. My distinction between “amateurs” and “non-amateurs” cuts across the distinction between people having a diploma or not having a diploma. Ramanujan is famous for his results in number theory, but did not have any formal training in mathematics. To make a living, he worked as a clerk in the accountant general’s office at the Madras Port Trust Office, see the Wikipedia on Ramanujan. It shows the open-mindedness of the community of mathematicians that Hardy invited him to come to Cambridge and discuss mathematical problems with him. None of the reluctance of Dutch lawyers to listen to Dutch statisticians.

If the the Hague Court or the committee Grimbergen now would come with: “Smits, Elffers and de Mulder are our Ramanujans of mathematical statistics!” (although, formally, in their point of view, they might find that they have no obligation to do this for the law psychologist Elffers, since he received a diploma in mathematics 30+ years ago), then we really have reached the end of the tunnel and can say: “Pardon me, papers of Ramanujan and Hardy have appeared in mathematical journals. Our profession of statistics has international journals like the Annals of Statistics, with refereed papers. Persons publishing in journals of this type, for example Richard Gill and Piet Groeneboom, to name just two, have looked at the work of your three Ramanujans and concluded that it is humbug. You should at least pay some attention to that!”.
The petition for reopening the Lucia de Berk can still be signed, see: Petition for reopening the Lucia de Berk case.


8 Responses to The Lucia de Berk case, part 2

  1. Dear Piet,

    Here are two more examples of the use of statistics in the verdict: (taken from my earlier postings in response to the Guardian article about the case, see )

    (1) indirect statistics

    One of the ‘murders’ concerns a 73-year old woman who suffered from terminal cancer. She was going to die soon, but when it actually happened, it was a bit sudden. The court asked six medical experts to give their opinion. Five say: this was a natural death. One says: at first I thought it was natural, but *given all the many other cases in which L. was involved*, I now think it was unnatural. The court follows this sole dissenting expert against the other five. But clearly, this dissenting expert uses a statistical rather than a medical argument! Since the court only listens to him and ignores the other 5 experts, the court is using statistics, once again. [I might add that this ‘murder’ was particularly important for the prosecution, because it was on the day that this woman died that Lucia wrote in her diary: ‘i have indulged in my secret compulsion today’. Lucia claimed she was writing about playing tarot with patients, but, because no patient could be found who would testify ever having played tarot with Lucia, they concluded that her ‘secret compulsion’ must refer to murder.
    Whatever her compulsion really refers to, given that (a) on the 8 other occasions she mentions it in her diary, no patient dies, and (b), 5 of 6 experts think the woman who died that day died of natural causes, the conclusion that the ‘compulsion’ must refer to ‘murder’ is quite amazing.]

    (2) the ‘chain proof’

    The court claims that for two of the 10 victims, they can actually prove murder by digoxin poisoning (in 1 case) and murder attempt by strangulation in the other case. So, according to them, these 2 cases have classical ‘beyond reasonable doubt status’. For the other 8 cases, they use something called a chain proof, a peculiar ‘tool’ in Dutch law. Basically it says that if you’ve been found guilty of a crime, and you’re a suspect in N more similar crimes, then the amount of evidence that constitutes ‘beyond reasonable doubt’ decreases with each further case. So for the second case, you need less evidence for the first. For the third, you need less than the second, etc.
    In Lucia’s case, for the eight subsequent cases, they only have ‘patient died or needed reanimation rather suddenly; no immediate cause could be found; some doctors think it might be an unnatural death; and Lucia writes about some secret ‘compulsion’ in her diary on some days, one of which happens to coincide with one of the deaths. In fact, for all these 8 cases, there originally was no suspicion at all (a natural death certificate was signed), all 8 cases were about VERY sick people, and in all 8 cases some doctors (often the majority of doctors asked!) still thought it was a natural death when they were asked in court (for some cases this was 5 years after the deaths happened).

    Now this chain proof construction may itself be thought of as a kind of flawed statistics, or at least, flawed ‘probabilistic reasoning’. From a probabilistic point of view, you can argue that the chain proof idea makes sense if you find 10 bodies ‘with knifes in their chests’, so to speak: if it is clear that 10 MURDERS have been committed, and you know that somebody was around during all of them, then it is indeed true that, given that is has been established that that person killed already two of them, then the conditional probability that the same person has killed the other 8 as well goes up tremendously. This reasoning is to some extent justifiable, if, for example,you assume that only a very small part of the population is murderous. (Let’s give a concrete but rough example. Let’s assume that not more than 1 in 10000 Dutchmen/women is mentally capable of murder. Suppose that 10 bodies have been found with knives in their chest. Let’s say that, at the time and the place of each of the murders, there were about 40 people nearby – about 40 people who ‘could have done it’. It has been established that Mr X killed two of the 10 dead people, and was around in all 10 cases; and that none of the other people who were around is known to be a killer Because it is known that Mr X is a killer, the conditional probability that he killed at least some of the other 8 people as well, GIVEN that he is a killer, and GIVEN that he was present at the other 8 cases, is quite high.

    The problem with the Lucia case is that there is hardly any evidence that these other 8 cases were murders/crimes. They may very well have been natural deaths. Under those circumstances, the chain proof construction makes no statistical/probabilistic sense at all. Many statisticians would object to the ‘Bayesian’ type of reasoning (using population base rates as a priori probabilities) which validates the chain proof argument in the case where there is no reasonable doubt that crimes have been committed; but note that such statisticians would doubt the validity of the chain proof *in general*. Such ‘frequentist’ statisticians would think that the chain proof argument is never valid. The Bayesian statisticians would think the chain proof is valid in *some cases*. I think that *no* serious statistician would think that the chain proof is a valid statistical/probabilistic argument in the present case, where it is not clear that crimes have been committed.

    Now I have been told that the chain proof is not a logic/probabilistic/statistical, but a *legal* argument. Maybe I’m naive, but if a logically invalid argument is used in court, then I think one should protest, even if that argument has the status of being ‘legal’.

    Peter Grunwald

  2. pietg says:

    Hi Peter,

    I want to comment on the expression “beyond reasonable doubt”. One of the lawyers, involved in the Lucia de Berk case, told prof. Richard Gill, when he was using the expression “beyond reasonable doubt”: “we do not make use of this concept in the Dutch law system!”. And indeed, if one looks at verdicts in Dutch Law cases, one notices that the expression “legally and convincingly proven” is used. So, apparently, this lawyer wanted to say to Richard Gill that “legally and convincingly proven” is different from “beyond reasonable doubt”. Is it a weaker statement, one wonders?
    For this very reason I was saying in my blog Lucia de Berk and the amateur statisticians about this concept: “I note in passing that the Dutch law system does not make use of this concept, I am sorry to say.”. Another lawyer, or at least a person who studied law in the Netherlands, reproached me in this context for “making irrelevant comparisons between the Dutch and English law system”. Is it irrelevant?
    Interestingly, we read on p. 10 of the verdict in the Lucia de Berk case under point 5.55: (I am forced to translate -a little bit- to the spirit rather than to the letter here, except for the statement in italics, which is a completely literal translation. If one can read Dutch one can check my translation on p. 10 of: the Hague Court verdict):
    “With respect to the question: “innocent or proven guilty” the Court used the following criteria:…
    A. There had to be a sudden and unexpected death or a life-threatening incident.
    B. There had to be a medically unexplainable death or a life-threatening incident where all relevant natural causes as mentioned above can be excluded beyond any reasonable doubt.” (Italics are mine.)
    This kind of thing is fairly typical for what happens if one gets into discussions with (certain) Dutch lawyers. A lawyer, involved in the Lucia de Berk case, says (see above): “We do not make use of this concept (i.e., “beyond reasonable doubt”) in the Dutch law system!”. With the implication: you should keep your mouth shut, you do not know anything about Dutch law. Then we look more closely into the phrasing of the verdict and, suddenly, we see this very expression appear in the verdict. What to think of that? I personally consider this as an encouragement not to keep my mouth shut!

  3. Richard Gill says:

    “Legal AND convincing proof” that you have done a crime, is subtly different from the “absence of reasonable doubt” that you did the crime. The Dutch system requires proof that is both legal and convincing, that you did the crime. If the defense has a good story which explains the evidence, then there is reasonable doubt that you did it. The evidence against you might well be legal but it is then not convincing, it is not compelling. You are not compelled to believe in guilt, if there is still a credible story built around innocence. The most senior Dutch lawyers I spoke to did agree with my point of view: Proof is not “convincing” if there is still room for “reasonable doubt”. However, law students are not aware of these subtleties (Prof. Willem van Zwet asked a class of law students, and they did not believe in “beyond reasonable doubt”).
    It seems many judges are not aware of it too. For instance in the Kevin Sweeney case, the prosecution simply did not try to discredit the defense’s position. Extremely expensive and complex experiments done by TNO on mimicking the fire which killed his wife Suzanne Davies, barely managed to show that the fire damage was consistent with arson. They had absolutely nothing to say about the question, whether the fire damage was consistent with an accidental fire. However this did not bother the prosecution or the judges in the least. The experiments were extremely expensive and the report on them is extremely long and technical. The summary contained the message which the prosecution and the judges wanted to hear, even though the content was in disagreement with it. The person running those experiments (who also did the experiments concerning the recent Schiphol fire) is well known “in the fire-safety trade” to be a charlatan. But he and his department have a monopoly position.

  4. Richard Gill says:

    PS I asked Willem van Zwet a few months ago to retell me this story about the class of law students. It turned out it wasn’t him wot posed the question to the students, but a friend of his – I think it was a well-known Leiden law professor who was dean of the law faculty at the time!

  5. Nico Roosnek says:

    I wish to express my very strong opinion: “Lucia de B. has been convicted without a fair trial”. One of the basic human rights has been violated: the right on a fair trial, see article 11 of the Universal Declaration of Human Rights.
    My opinion is based on 100 % proven medical, pharmacological and statistical facts, which show that there were no murders. Besides no murders, there were no means or traces of murder found justifying any suspicion. Moreover, Lucia de B. had a lot of empathy for very sick patients (how nice to have a nurse with empathy). When ‘they’ got the opinion that she differed from the group and more deaths occurred when she was in the neighborhood, which might happen to one out on nine nurses (see One in nine nurse go to jail), there had to be some black magic surrounding her. The causes of death, in the hospital classified as natural, were changed into unnatural, when Lucia happened to have beeen in the neighborhood. If that had been the case, the unnatural causes were changed into murder. Who would one think was without any doubt the murderer? Indeed, Lucia.
    The gullibility of the members of the hospital, the police, prosecution, the District Court, Court, Supreme Court of Justice is quite amazing, but that is another matter. What is perhaps worse however is that Paula Lampe, a self-declared psychologist, gave the motive for the murders, based on kitchen psychology. Using this type of information, one is, before one knows, considered to be a serial murderer, going for her/his victims.

    Now three wise man, in a committee, considering the case for a possible reopening, have reported that a number of facts is not true. But there remain some facts, they say, which are not clear! So a small enquiry, causing further delay, has been started before submitting a request to the Supreme Court for reopening the case! There is nothing left to be cleared! A number of university professors is eager to advice anybody on this point.
    The adviser of the Prosecution gave a short while ago a very remarkable presentation on television. With reddening eyebrows (a sign of …, ask Lampe) he told his unworthy tale that there is still something fishy in the case, as the three wise men thought, which had to be cleared first. This will of course cause further delay.
    When the parliamentarians were asked to look at these cases, they answered in choir with the incantation: “Trias Politica”.
    Lucia was convicted without a shred of evidence, that is my opinion. Please let anybody come forward to me with that shred of evidence, if he thinks otherwise.
    My quest is to have Lucia freed from the thought let alone the conviction of any wrong doing. I still remain with one question: “Why does the whole system not work?”. This can happen to anyone, also to you.

  6. pietg says:

    Yes Nico, the incantation “Trias Politica” has become the “easy way out”. This once had a good effect. But in the Netherlands it is presently used against any non-lawyer who dares to have an opinion on a law case. In surrounding countries there are still juries, laymen judges, etc., but in the Netherlands the third pillar of the Trias Politica in in full power, without any input from outside. Many people (even some lawyers) think that this is a very undesirable situation. The way the Lucia de Berk case has been treated illustrates how bad the present situation is.

  7. nico says:


    Did you read about the resurrection of a great mathematician? There is also a reference to an article why he went into hiding in the next link.
    Altogether remarkable. It shows that Lucia was lucky that there was a woman that did not believe the awkward story, that was told to her in the family.

  8. pietg says:

    I took a brief look at:
    and I must say that it looks somewhat suspicious to me…

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