Richard D. Gill's home page
You can read my "farewell lecture" (September, 2017) at
To contact me quickly, try email
(surname at math dot leidenuniv dot nl), or mobile phone.
Click here for my postal and visiting addresses,
mobile phone number, various other email addresses and other contact possibilities.
In particular, I have started a one man statistical consultation business
Combray Causality Consulting.
Every statistician in the world is currently working on the Corona crisis.
I have been looking at the results of the Marseilles trial of
hydroxychloroquine and azithromycin in very early Covid-19 infection. I've also
been studying the data of Dutch GP Rob Elens. A conference talk for the
Bernoulli-IMS One World Symposium (August 2020) is in preparation.
Here is a preview of the slides of my talk Presentation.pdf
(recently updated) and here is the
video presentation (youtube video).
Here is a short version of the slides
(for a three min "elevator pitch"). Here is a
short intro to who I am.
Here are some preliminary analyses with R and with JASP:
raoultJASP.html. More to come, soon.
And a recent talk "Corona statistics, Corona uncertainty"
video of part 2; open discussion.
Part 1 of the video to be added, soon.
See also Rob Elens data analysed
and open letter to NEJM.
A Zoom commemoration of W.R. van Zwet (207 MB mp4;
duration 35 minutes; 5 minutes silence between ca. 25 - 30 min. when Zoom briefly fails us).
Photographs collected by many friends of Willem:
Blog posting, "RIP Bill van Zwet"".
I have revised and extended my farewell lecture
"From killer nurses to quantum entanglement",
and am slowly converting it into a new paper
"Statistical issues in Serial Killer Nurse cases"
with amazing new statistical graphics on the (UK) Ben Geen case.
Latest version: 14 February 2020, email me if you want to see it.
See also my recent Ben Geen talk. Here are links to
the expert opinion of
Jane Hutton and the
expert opinion of
Professor David Denison
(who sadly died in 2014)
at Ben's appeal in 2009 concerning the statistical, or rather scientific issues,
around "unexpected clusters of medical cases" and their association with
particular health care workers.
The judge did not allow Jane to summarise her "Opinion" (technical term for an
expert's report) in court in person because it was "merely common sense",
as was also Denison's Opinion. At the judge's summing up, the jurors were
instructed to ignore that evidence. No common sense in my court, please! (shades
of Sally Clark: it was "not rocket science"). This obviously unfair legal ruling
provided Ben's legal team with legal grounds for approaching the CCRC
and hiring me: I was to perform the epidemiological
research which Jane had argued needed to be performed.
I'm a member of the North Sea Group,
a circle of scholars and scientists mainly from countries around the North Sea,
interested in legal evidence and legal proof.
We have a webpage with blog and
The group has been meeting at annual workshops already for several years.
A speciality is to study specific cases in depth using
different methodologies from computer science and artificial intelligence,
from psychology, philosophy and law, from statistics and probability.
Some thoughts on Bell’s theorem & on Bell-denialism,
Zoom.us talk at QM foundations – nature of time seminar, J U Krakow, 5:00 p.m. Warsaw time, April 6, 2020.
Krakow talk, continued,
Zoom.us talk at QM foundations – nature of time seminar, J U Krakow, 5:00 p.m. Warsaw time, April 13, 2020.
Blog instalment "Warsaw"
Yet Another Statistical Analysis of the data of the (2015) "Loophole-Free" Bell-CHSH Experiments,
Vaxjo "QIRIF" conference, June 2019.
Lecture course "The Role of Statistical Science
in Quantum Information", given at Fudan University, Shanghai,
and Peking University, Beijing, September/October 2019.
Illustrations: the satellite Micius was used in Jianwei Pan's
Earth (Shanghai) - Space (Micius) - Earth (Beijing) quantum key-distribution
experiment in 2017. Here are a links to directories containing materials for the courses at
Fudan University and at Peking University.
I will continue to organise this material and perhaps write a small monograph in
"lecture notes" style.
Foraging for wild mushrooms.
The intersection axiom of conditional independence.
Dutch New Herring, correlation vs causation, good scientific research practices.
It is getting hard to find the two Tilburg University press releases
and economist Ben Vollaard's two "AD Haringtest" papers on internet, so here are links:
AD Haringtest paper July 2017,
AD Haringtest update November 2017,
Press Release July 2017,
Press Release November 2017.
I will put the links into the slides, as well as update with my latest research findings
on time-dependence through self-selection of participants and panel: the "samples" are
not random samples.
I had a conflict of interest - I was asked in 2018 for my scientific opinion on the
original papers by one of the parties in the ensuing legal (scientific integrity) case.
The original documents are all in Dutch. For three years, Dr. Vollaard declined to
share the data-sets which he analysed. The Dutch national institution for dealing with
alleged failures of scientific integrity (LOWI) has in October 2019 (advice no. 23)
concluded its work on the case. The conclusion can be found (anonymised) on their website.
LOWI writes "The LOWI would applaud it if a scientific debate could take place
between all parties involved, and experts". They also write "It is clear that mistakes
were made in the press release which presented the results of this research
to the public". The data-sets can at last be downloaded from Dr. Vollaard's personal
webpage. Unfortunately they are in the proprietary format of the commercial "Stata"
package, which I do not wish to pay for. Fortunately, Stata data files can now be fairly
easily read into R and converted to non-proprietary formats.
I can email a csv file to anyone interested.
26 August, 2015. They did it at last! A first reaction.
What did they do, exactly, and what was my (modest) scientific
Illustrations: Figure 7 from "Bertlmann's socks and the nature of
reality", Bell (1981); and the set-up in Delft, 2015.
See "Bell games" for a comparison of the standard Bell
experiment and the Delft "event-ready detectors" version built on top of
Interview with John Bell (OMNI, 1988)
Quantum Love (Delft YouTube video
I must admit to getting a lot of fun, and scientific stimulation, from
interacting with Bell-deniers. I apologise for the names I use. It can be argued that
such derogatory terms do not belong in civilised public scientific conversation,
but unfortunately they are common in private conversation,
which of course is also part of science. I feel that those who suspect that such labels
are being applied to them should proudly wear them
as badges of honour. As Gandhi said: first they ignore you, then they fight you,
then you win. When they call you names, it means you are somehow a threat to them.
It might mean that they are losing the argument.
In fact, I consider this an important part of science-outreach:
how can we explain Bell's theorem to the general public?
Well, a good start is to try to understand the mentality of very smart and
well-educated people who believe that Bell made some fundamental but simple
mistake, that they have exposed that mistake, and that there is an establishment
conspiracy to suppress their findings. I believe that Bell's argument is very simple
and absolutely correct, but apparently it is hard to get across.
Part of the problem is, I believe, the fact that it is impossible to
"understand" quantum mechanics, in the sense that we usually use the word
"understand". In fact, that is exactly the content of Bell's theorem. A "local realistic"
interpretation of quantum mechanics is precisely:
an interpretation that we can understand. We can get used to the mathematics, we can
even gain intuition about the the *mathematical world* which the conventional rules of
quantum mechanics describes. But those rules will never make sense as a picture of how
the world actually operates.
The images below come from a new version of a paper I wrote a few years ago entitled
"The triangle wave versus the cosine".
The paper studies the "spinning coloured disk model" of the so-called EPR-B correlations.
It is about the class of all correlation functions
which classical physics can generate, in a situation when we expect certain
symmetries and "certainty relations". The paper describes many open problems in classical
probability theory, some inspired by looking at computer simulations.
I was asked by defense lawyers
working on behalf of Ben Geen, to analyse statistical data of
occurrence of respiratory arrest in accident and emergency at numerous
(draft R html notebook,
After I had done my statistical work, I dug more deeply into
other aspects of the case. The more I discovered, the more I was shocked that
this case was a carbon copy of our own (Netherlands) case of Lucia de Berk.
However there are three important differences. (1) The UK media did an even more
perfect hatchet job on him than the Dutch media did on Lucia. (2) The Criminal Cases
Review Commission is understaffed and underfunded, and takes a formalistic (legalist)
view: give us a "new legal fact" or we will do nothing. (3) There is no Metta de Noo:
no medical whistleblower. In the Lucia case, Metta de Noo fought for 7 years to get
Lucia the fair (re-) trial which Lucia deserved. Metta is a senior medical expert,
well connected in society, and she had inside information about the case.
In the Lucia case, what was needed (and finally happened at the re-trial in Arnhem,
2009--2010) was an independent and thorough re-appraisal of
existing (medical) evidence.
Ben has by now sat out about 12 years of his 30 year sentence.
Because he claims to be innocent
he is denied any "good prisoner" benefits and
will also never get parole or early release.
A small supporters' group set up a website
Justice for Ben Geen.
Some UK journalists, at "The Times" no less,
briefly showed some interest:
Nurse 'was victim of Shipman hysteria'
For a long time nothing has happened but right now, things are moving again.
YouTube video. Slides of my talk
Murder by Numbers.
The naked truth about the case of Lucia de B.
A historical document: statement by Haga-Hospital, 2010,
regarding the acquittal of Lucia de Berk:
Four days after the TEDx event, I saw the movie Lucia de B.
on its premiere night in Amsterdam. Here is my personal
film review: Splendid acting, very moving, beautifully told human story,
centering around Lucia herself. Despite compression of the story line and focus
on Lucia's personal experiences, it still contained such key features as:
the close personal links
between key people from hospital, justice and experts (image right);
the mental illness and mental breakdown of the chief-paediatrician at JKZ ...
There was a vain and ambitious hospital director. A bad statistician.
Real life heroine Metta de Noo and hero Ton Derksen
were concentrated in the film into the imaginary person
of one imaginary whistleblower at the last place you might expect
to find them: in the Public Prosecution service. But on the other hand:
it wasn't black and white. There were good medics and bad medics,
good nurses and bad nurses, good cops and bad cops ... Apparently,
even some people in the Public Prosecution service found the witch hunt
For more (much, much more) on the Lucia case,
see several more items below, as well as yet more
items from past versions of my home-page:
writings on Lucia.
Some years ago
I offered a prize for the person who remasters the logo of the
VVS: the Dutch statistical society
(top image) in the most beautiful postscript. An exercise in
curve fitting with splines, perhaps?
Better still would be a mathematical/statistical story of the curves
themselves, providing an elegant parametric family which reproduces the
whole logo. Finally I decided to do it myself, and I think I am getting
close with this perspective image of some very simple 3-dimensional
curves, with indeed a statistical story behind them
The R script which draws this logo can be found here.
It should generate a rotatable 3-d image...
See the slides of my
Amst-R-dam R users group meetup 2011
(updated 2012) talk
R-fun: part 1, the VVS logo in R; part 2, R on an iDevice.
For some old news on "R on an iDevice" see the 2014 talk
R on an iDevice,
given at a Data Science NL meetup.
For more R fun: I am nowadays an enthusiastic user of RStudio and RPubs.
You can find all kinds of
R work by me at my RPubs site.
VVS stands for "Vereniging voor Statistiek". SMS stands for
"Section Mathematical Statistics".
The VVS also has an OR section, hence the common alternative name VVS-OR. And nowadays
the society has a nice new logo, though it doesn't look to me so much
like anything to do with statistics
Teaching (already seems like long ago!)
FSG: Tuesdays 13:45--15:30 room 405
Master's level (or advanced Bachelor's)
The master specialization Statistical
Science for the Life and Behavioural Sciences is a collaboration of our group with
others in biomedical statistics, biostatistics, and psychometrics.
Here you can find links to various courses I have given in the past,
in particular quantum statistics,
statistics for astronomers,
HOVO courses (adult education courses, in Dutch) on
use and abuse of statistics, forensic science
For some outdated impresions of my research interests,
take a look at various talks on
My last PhD student was
working on forensic statistics,
in particular the rare haplotype problem (aka the "fundamental problem
of forensic mathematics"). Giulia was in a "cotutelle" arrangement:
this was a joint project between Lausanne (Franco Taroni) and Leiden.
Interests (somewhat out of date), most active marked *
Not so recent talks and papers
WARNING: Richard P. Feynmann said
that attempting to understand quantum mechanics causes you
to fall into a black hole, never to be heard from again
The past is particles, the future is a wave
Bell's fifth position
During the academic year 2010-2011 I was
Distinguished Lorentz Fellow
(DLF) at the Netherlands Institute of Advanced Study in the Humanities and Social Science,
Here's my research proposal.
The award ceremony was at NIAS, Wassenaar, late-afternoon of March 22, 2010.
On the morning of the same day we held a complementary
Breakfast symposium "Science, Media, Justice"
The Smeesters affair (revised: July 4, 2013)
Slides of talk on Smeesters case, and on the Geraerts-Merckelbach Memory paper affair.
Talk originally given December 2012; slides updated March 2013; title
"Integrity or fraud - or just questionable research practices?"
Stimulated by media interest in the Geraerts-Merckelbach controversy on their
"Memory" paper, I studied the published summary statistics in this paper
using the same techniques as Simonsohn used for Smeesters, and found quite clear
statistical evidence for "too good to be true". Without
experimental protocols written up prior to the experiment, original data-sets,
and laboratory log books detailing all the data selection and manipulation steps
which resulted in the final data-set on which the summary statistics
in the paper are based, one can only guess how these patterns arose.
It certainly need not be fraud (fraud requires active intention to deceive).
R-code for experiment with Simonsohn's fraud test (new version)
Histogram of p-values of an honest researcher
Histogram of p-values of a dishonest researcher
You can continue reading here
Various (updates badly needed to many of these items)
Biography and more ...
First Leiden inaugural lecture
Past phd students
Just for fun:
things you wish your computer had
(including the classic clippy's suicide note)
A few years ago I discovered the enormous disussion on the
Monty Hall (three doors) problem on wikipedia.
My published writings on the subject are, in order of writing (and in order of
insightfulness) an invited contribution to
Springer's International Encyclopaedia of Statistical Science, 2010,
a paper in Statistica Neerlandica, 2011,
and contributions to the peer reviewed internet encyclopedias
In this manuscript you will find
an expanded version the most recent published work, the
In these works I distinguish between the original, somewhat
ambiguous, real world question about a famous quiz show, and the many
mathematizations of the question which
have been proposed in the literature. Personally I prefer the lesser
theoretic version. For me, the question is not "what is this
probability?" or "what is that probability?", but: "what would you do?"
And to me, the wikipedia controversy around
the Monty Hall problems (concerning whether we should compute a
conditional or unconditional probability of getting the car if we
switch doors) is a warning against solution-driven science.
I want to thank so many wikipedia editors for the inspiration they gave
Suppose the car is hidden behind one of the three
doors by a fair randomization. The contestant chooses Door 1. Monty
Hall, for reasons best known to himself, opens Door 3 revealing a goat.
We know that whatever probability mechanism is used by Monty for this
purpose, the conditional probability that switching will give the car
is at least 1/2. We know that the unconditional probability (ie not
conditioning on the door chosen by the contestant, nor the door opened
by Monty) is 2/3.
Always switching gives the car with unconditional probability 2/3,
always staying gives it with probability 1/3. Nobody in their right
mind could imagine that there could exist some mixed strategy
(sometimes staying, sometimes switching, perhaps with the help of some
randomization device, and all depending on which doors were chosen and
opened) which would give you a better overall (ie unconditional) chance
than 2/3 of getting the car.
This is true, of course. In fact, from the law of total
probability, proving the optimality of (unconditional) 2/3 by always
switching is equivalent to proving that all the six conditional
probabilities of winning by switching, given door chosen and door
opened, are at least 1/2. We can prove the latter using Bayes' theorem,
or, better I think, using Bayes' rule in a smart way. However both
these proofs require some sophistication.
Is there an elementary proof? A short proof using words and ideas, no computations.
Yes there is, and I learnt it from Sasha Gnedin.
However you play there's always a door such that if the car is
there, you'll miss it. Consider first deterministic strategies. We only
need consider two cases: for "always switching" it's the door you
initially chose, and for "sometimes switching" it's a door you won't
switch to if you get the option. (If you never switch there are two
such doors: just choose one). Ordinary readers won't be interested in
randomized strategies but anyone who wants to include these will
understand how to do it (now the door where you'ld certainly miss a car
has to be a random door, determined by the same coin tosses used to
implement the random choices in your own strategy).
Note that the door which has been indicated in this way does not
depend on where
the car is actually hidden or how the host plays: it just depends on
how the player plays. Therefore if the car is initially equally likely
to be behind any of the three doors, we run a 1/3 chance that the car
will be missed because it's behind this door. Therefore the 2/3
success-chance of always switching can't be beaten.
I would call this a proof by coupling.
From Three Doors to Two Envelopes (what will be next? One Coffin, perhaps?).
Here is the definitive article on the infamous two
envelopes problem. The problem which Martin Gardner could not solve,
and which many other famous people got wrong. Studied by probabilists
(both Bayesian and frequentist), logicians, economists, philosophers.
Now studied by me ...
The mathematical heart of all exchange paradoxes
is encapsulated in a little theorem which I call my
"unified solution". It seems to be new.
Lucia de Berk
The tunnel-vision which characterized Lucia's case was cemented in the two
weeks around "the" nine-eleven inside a hospital in the Hague.
Once by the end of those two weeks a major
medical institution had (by implication)
told the world that it had caught a serial killer,
it must have been very hard for those who brought
charges - a few individuals at the
very top of the very same institution -
not to have had some large influence, deliberately or innocently,
on the results of police investigation,
and on the "medical" interpretation of the medical dossiers which
went to the courts. The events of the past year
which came up during those two weeks of internal investigation
and suddenly associated with Lucia
had become unexpected and inexplicable,
though previously every single one of them had been unremarkable.
The hospital investigators into
the crime were the same people earlier treating those patients, and making,
as is completely natural, errors of diagnosis or treatment from time to time.
The collegiality of the medical community means
that mistakes by medical specialists within the Netherlands
can hardly be admitted by
others inside the same relatively tight, and extremely powerful, community.
Highly placed medical authorities had to stand firm
by their own previous and now provenly mistaken diagnoses. Others
would be loath to criticise a highly regarded colleague's decisions
in such a critical case.
In the Netherlands, medical practitioners almost never admit to having made
mistakes... consequently, they do not have to insure themselves agaist being sued
for malpractice (which is good for their income), and in theory
medical treatment should be less expensive than in other countries
where lawyers and insurance companies profit from medical missers.
However the Dutch arrangement has led to increasing distress among all
those "victims" of medical errors, many of whom would probably be satisfied just
to have an "accident" admitted! This June 16, a new code of practice has been
introduced, by which medical practitioners will in future be able to apologize for errors
without thereby admitting legal responsibility. A giant step for the medical profession,
though only a very small step for their patients. Better than nothing, or merely a crumb
to keep us "consumers" (the ones who pay for health care) quiet?
Many years after judicial authorities apologized personally and publicly,
it is still high time to start finding out
where avoidable mistakes were made. It is hard
to believe that these can only be attributed to police investigation
and legal procedures. However that is the implication of the
statement by the board of Lucia's hospital,
(unauthorized rough English translation).
Statistical ethics of the probiotica trial.
This randomized triple-blind clinical trial of probiotics treatment
for patients with predicted severe acute pancreatitis ended in controversy,
when it transpired at the conclusion of the trial in
December 2007, that rather more patients had died on the treatment
arm of the trial than on the control arm.
It seemed strange that the trial had not been terminated at the
interim analysis. The researchers were using a a stopping rule
of S.M. Snapinn, by which the trial would
to be terminated early either if it were almost certain that the
final result would be a significant positive effect of probiotica,
or if it were almost certain that the final result would be insignificant.
Here is a paper by myself, to appear
in Statistica Neerlandica,
and, in Dutch, a short article by
probabilist Ronald Meester and microbiologist Pieter ter Steeg which
appeared in the newspaper Trouw and an
to Meester and ter Steeg
by biostatisticians Hans van Houwelingen and Theo Stijnen.
Also in Dutch there are a series of interviews (early 2008)
on the current affairs chat show
'Pauw and Witteman':
chairman of the hospital board Geert Blijham, 23 January;
patient Jochim Vromans, 24 Jaunary;
probiotics expert Eric Claassen, 25 January;
leader of the research team Hein Gooszen, 14 February.
Later we obtained the data at the time of the interim analysis.
It was given to journalists at a press conference on Feb. 13 2008,
but never released to interested scientists.
It turned out that the probiotica trial was
not terminated for futility (following the Snapinn stopping
rule) at the half way interim analysis,
through a mis-reading of output of the SPSS package,
which, without consulting the user,
always reports the smaller p-value of the
two one-sided Fisher's exact tests for
equality of two binomial probabilities. Proper application of their
own stopping rule would have led to early termination of the trial,
since according to the criteria set in advance,
there was no chance any more that it would result in a positive
result for the probiotica treatment. The trial
was de facto continued because there was a good chance that it
would finally result in a negative result for probiotica.
Here are slides
of my talk careless statistics costs lives
on the subject.
Mathematical Centre (Amsterdam) publications are now available on internet.
Here are two early works which had quite some impact, including
the reprint of my 1979 PhD thesis:
R.D. Gill (1980),
and Stochastic Integrals, MC Tract 124.
R.D. Gill (1983),
sieve method as an alternative to dollar-unit
sampling: the mathematical background, Report SN 12
Another useful link is to my
Saint Flour lectures on survival analysis.
Product-integrals are to
products, as integrals are to sums. Though they have been around for
more than a hundred years, they never became part of the standard
toolbox, possibly because no-one invented the right mathematical symbol
for them. I made a try quite some years ago, though they still have not
caught on yet. With the crucial help of JC Loredo, my efforts resulted
prodint.zip, files for getting beautiful
\prodi and \Prodi and \PRODI symbols in your LaTeX, and Loredo.ttf,
a TrueType font for ordinary word processing. It is not that difficult
these days to get new fonts into your latex, see for instance TUG's
font installation instructions.
My sanskrit name
Sarasvati Leela dasa (dasa: a devotee; Leela: games; Sarasvati:
goddess of science, music, self-knowledge)
My Korean signature
(Last updated: 18 October 2020)