Richard D. Gill's home page

Mathematical Statistics

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 contribution.



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 entanglement swapping.



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 UK hospitals (draft R html notebook, draft report). 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.

R-fun

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 (bottom). 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!)

Spring 2016





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 (Hovo-criminalistiek-statistiek-1, Hovo-criminalistiek-statistiek-2, Hovo-criminalistiek-statistiek-3).

Research

For some outdated impresions of my research interests, take a look at various talks on Slideshare.

Interests (somewhat out of date), most active marked *

causality, graphical models, forensic statistics, forensic DNA, statistics and law, scientific integrity and scientific fraud, science and society *** quantum statistics, probability, information, foundations * statistical and computational learning * missing data, censoring * survival analysis, semiparametric models, martingale methods, counting processes, non parametric maximum likelihood product integration, compact differentiation, the delta method, the bootstrap, empirical processes in statistics spatial statistics and image analysis random number generation mathematical typography foundations of statistics, probability, mathematics, quantum theory (see middle of this page) *

Not so recent talks and papers

Publications

Papers in quantum statistics (arXiv:quant-ph) Recent papers in mathematical statistics (arXiv:stat) Publication list, including prepublications and unpublished work Links to many of my older papers can be found via the MC and CWI repository

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

The Smeesters affair (revised: July 4, 2013)

Various (updates badly needed to many of these items)

First Leiden inaugural lecture

Curriculum Vitae

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)

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.

The mathematical heart of all exchange paradoxes is encapsulated in a little theorem which I call my "unified solution". It seems to be new.

Various

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 open letter 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), Censoring and Stochastic Integrals, MC Tract 124.

R.D. Gill (1983), The 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 in 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

My Korean signature