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Richard Gill

Universiteit Leiden, Mathematical Institute, Faculty Member

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I'm a retired professor of mathematical statistics, interested especially in quantum information and the foundations of quantum mechanics, in forensic statistics, and in scientific integrity.

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Papers by Richard Gill

Healthcare serial killer or coincidence? Statistical issues in investigation of suspected medical misconduct

Cornell University - arXiv, Oct 3, 2022

Justice systems are sometimes called upon to evaluate cases in which healthcare professionals are... more Justice systems are sometimes called upon to evaluate cases in which healthcare professionals are suspected of killing their patients illegally. These cases are difficult to evaluate because they involve at least two levels of uncertainty. Commonly in a murder case it is clear that a homicide has occurred, and investigators must resolve uncertainty about who is responsible. In the cases we examine here there is also uncertainty about whether homicide has occurred. Investigators need to consider whether the deaths that prompted the investigation could plausibly have occurred for reasons other than homicide, in addition to considering whether, if homicide was indeed the cause, the person under suspicion is responsible. In this report (commissioned by the Section on Forensic Statistics of the Royal Statistical Society, London) we provide advice and guidance on the investigation and evaluation of such cases. Our work was prompted by concerns about the statistical challenges such cases pose for the legal system.

The Monty Hall Problem is not a Probability Puzzle

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a c... more Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? The answer is "yes" but the literature offers many reasons why this is the correct answer. The present paper argues that the most common reasoning found in introductory statistics texts, depending on making a number of "obvious" or "natural" assumptions and then computing a conditional probability, is a classical example of solution driven science. The best reason to switch is to be found in von Neumann's minimax theorem from game theory, rather than in Bayes' theorem.

Product-integrals and counting processes

The Cochran-Mantel-Haenszel test and the Lucia de Berk case

The asymptotic power of the Mantel-Haenszel test is compared to that of its competitors.

Comment on "When Quantum Computation Meets Data Science: Making Data Science Quantum

arXiv: Quantum Physics, Nov 11, 2021

I draw attention to statistical and probabilistic and computer science aspects of the very, very ... more

Better Bell Inequalities

I explain quantum nonlocality experiments and discuss how to optimize them. Statistical tools fro... more

Optimal Design of Bell Experiments

Contributions to Statistics

ABSTRACT In this paper, we discuss quantum nonlocality experiments and show how to optimize them ... more ABSTRACT In this paper, we discuss quantum nonlocality experiments and show how to optimize them in respect of their experimental setup. The usage of statistical tools from missing data and maximum likelihood are crucial. An aim of this paper is to bring this kind of theory to the statistical community.

The model of Latent Structure Analysis

Statistica Neerlandica, 1976

A practical consultation problem is used to explain and illustrate the model of latent structure ... more A practical consultation problem is used to explain and illustrate the model of latent structure analysis. After an introduction, the model, its identification, estimation and testing are discussed; in a final section the hypothesis that visually handicapped people can be classified as "plucky" or "not plucky" is investigated.

An Elementary Approach to Weak Convergence for Quantile Processes, With Applications to Censored Survival Data

Journal of the American Statistical Association, 1992

Page 1. An Elementary Approach to Weak Convergence for Quantile Processes, With Applications to C... more

Octane number prediction based on gas chromatographic analysis with non-linear regression techniques

Chemometrics and Intelligent Laboratory Systems, 1994

Most widely used techniques for multivariate modelling (principal component regression (PCR), par... more Most widely used techniques for multivariate modelling (principal component regression (PCR), partial least squares (PLS)) are based on linear relations between variables. They are also applied when the chemical or physical relations underlying the data are known to be of a non-linear nature which leads to sub-optimal models. In case of non-linearities possible alternatives are the use of projection pursuit regression and neural networks. Projection pursuit regression is based on a 'projection' of the independent variables on direction vectors that are found ('pursued') using a gradient descent optimization technique. The projected independent variables are smoothed to include any non-linearities. The smooths can be represented graphically which enables visual inspection of the non-linearities. Neural networks are based on simple processing units that contain a non-linear transformation function. Connecting a number of processing units and estimating the weight of each connection is the basis of the neural network. Estimating the weights by repeated adaption of their value after a number of example cases have been presented allows non-linear relations to be modelled. The non-linear techniques are applied to the results of gas chromatographic analysis of gasolines. The results of the mass distribution of the gasolines over numerous individual components are combined into so-called PIANO groups and related to octane numbers. The octane number of gasolines is known to depend non-linearly on the specific composition of the gasoline. A data set of 824 gasolines, each separated in 89 PIANO groups is used. For each gasoline, the octane number is known. It is shown that projection pursuit regression and neural networks can be used to model the relation between PIANO groups and the octane number. * Corresponding author. gasoline is determined by the measurement of a standard knock intensity in test engines, where the sample's performance is compared to reference fuel blends [l]. One of the critical points of this method is the consumption of 500 ml of naphtha per measurement. Another is that the minimal standard deviation of the test is 0.3 point. In practice, two octane numbers are used, the

Analyzing Bivariate Continuous Data Grouped into Categories Defined by Empirical Quantiles of Marginal Distributions

Biometrics, 1997

Epidemiologists sometimes study the association between two measurements of exposure on the same ... more Epidemiologists sometimes study the association between two measurements of exposure on the same subjects by grouping the original bivariate continuous data into categories that are defined by the empirical quantiles of the two marginal distributions. Although such grouped data are presented in a two-way contingency table, the cell counts in this table do not have a multinomial distribution. We describe the joint distribution of counts in such a table by the term empirical bivariate quantile-partitioned (EBQP) distribution. Blomqvist (1950, Annals of Mathematical Statistics 21, 539-600) gave an asymptotic EBQP theory for bivariate data partitioned by the sample medians. We demonstrate that his asymptotic theory is not correct, however, except in special cases. We present a general asymptotic theory for tables of arbitrary dimensions and apply this theory to construct confidence intervals for the kappa statistic. We show by simulations that the confidence interval procedures we propose have near nominal coverage for sample sizes exceeding 60 for both 2 x 2 and 3 x 3 tables. These simulations also illustrate that the asymptotic theory of Blomqvist (1950) and the methods that Fleiss, Cohen, and Everitt (1969, Psychological Bulletin 72, 323-327) give for multinomial tables can yield subnominal coverage for kappa calculated from EBQP tables, although in some cases the coverage for these procedures is near nominal levels.

Censoring and Stochastic Integrals

Journal of the American Statistical Association, 1982

CHAPTER 2. SOME RESULTS FROM THE THEORY OF STOCHASTIC PROCESSES 2. 1. Notation and basic concepts... more CHAPTER 2. SOME RESULTS FROM THE THEORY OF STOCHASTIC PROCESSES 2. 1. Notation and basic concepts. 2.2. Stochastic integrals 2.3. Counting processes. 2.4. A martingale central limit theorem and related results CHAPTER 3. RIGHT CENSORED OBSERVATIONS AND STOCHASTIC INTEGRALS 21 3. 1. Background. . •. .. .. . •. .. 21 3.2. One sample case: the product limit estimator. 3.3. Two sample case: the test statistics of Gehan, Efron and Cox. CHAPTER 4. ASYMPTOTIC RESULTS 4.1. Consistency of the product limit estimator and of test statistics of the class K+. .. .. 4.2. Weak convergence: general theorem and product limit estimator •. .. .. . 4.3. Weak convergence: test statistics of the class K CHAPTER 5. EFFICIENCIES AND NEW TEST STATISTICS. 5.1. Introduction; comparison of variance estimators. 5.2. Efficiencies. . 5.3. Optimal tests of the class K for parametric alternatives 5.4. Renyi-type tests CHAPTER 6. GENERAL CENSORSHIP AND TRUNCATION.

Healthcare serial killer or coincidence? Statistical issues in investigation of suspected medical misconduct

Justice systems are sometimes called upon to evaluate cases in which healthcare professionals are... more Justice systems are sometimes called upon to evaluate cases in which healthcare professionals are suspected of killing their patients illegally. These cases are difficult to evaluate because they involve at least two levels of uncertainty. Commonly in a murder case it is clear that a homicide has occurred, and investigators must resolve uncertainty about who is responsible. In the cases we examine here there is also uncertainty about whether homicide has occurred. Investigators need to consider whether the deaths that prompted the investigation could plausibly have occurred for reasons other than homicide, in addition to considering whether, if homicide was indeed the cause, the person under suspicion is responsible. In this report (commissioned by the Section on Forensic Statistics of the Royal Statistical Society, London) we provide advice and guidance on the investigation and evaluation of such cases. Our work was prompted by concerns about the statistical challenges such cases pose for the legal system.

Healthcare serial killer or coincidence? Statistical issues in investigation of suspected medical misconduct

Justice systems are sometimes called upon to evaluate cases in which healthcare professionals are... more Justice systems are sometimes called upon to evaluate cases in which healthcare professionals are suspected of killing their patients illegally. These cases are difficult to evaluate because they involve at least two levels of uncertainty. Commonly in a murder case it is clear that a homicide has occurred, and investigators must resolve uncertainty about who is responsible. In the cases we examine here there is also uncertainty about whether homicide has occurred. Investigators need to consider whether the deaths that prompted the investigation could plausibly have occurred for reasons other than homicide, in addition to considering whether, if homicide was indeed the cause, the person under suspicion is responsible. In this report (commissioned by the Section on Forensic Statistics of the Royal Statistical Society, London) we provide advice and guidance on the investigation and evaluation of such cases. Our work was prompted by concerns about the statistical challenges such cases pose for the legal system.

Quantum Computation, Data Science, and Bell games

Quantum computing seems to be on the way, but still there are many hurdles to overcome and still ... more Quantum computing seems to be on the way, but still there are many hurdles to overcome and still there are some who have fundamental doubts that it will ever deliver the goods. In the meantime, a parallel research effort is being made in designing and implementing quantum internet. How about the prospect of uploading a quantum state to a quantum computer over a quantum communication channel? In fact, that is exactly what quantum teleportation is about. Quantum internet could also have application in generating shared classical cryptographic keys in a way which ensures that two distant parties can each be sure of having a copy of the key, and simultaneously be sure that nobody else can know it. I make a connection between quantum internet and one of Yazhen Wang’s topics, namely the topic of Bell games. Already, collaboration between statisticians and probabilists on the one hand, and quantum physicists both experimental and theoretical on the other hand, has led to important developm...

Statistical Analyses in the case of an Italian nurse accused of murdering patients

Suspicions about medical murder sometimes arise due to a surprising or unexpected series of event... more Suspicions about medical murder sometimes arise due to a surprising or unexpected series of events, such as an apparently unusual number of deaths among patients under the care of a particular nurse. But also a single disturbing event might trigger suspicion about a particular nurse, and this might then lead to investigation of events which happened when she was thought to be present. In either case, there is a statistical challenge of distinguishing event clusters that arise from criminal acts from those that arise coincidentally from other causes. We show that an apparently striking association between a nurse's presence and a high rate of deaths in a hospital ward can easily be completely spurious. In short: in a medium-care hospital ward where many patients are suffering terminal illnesses, and deaths are frequent, most deaths occur in the morning. Most nurses are on duty in the morning, too. There are less deaths in the afternoon, and even less at night; correspondingly, less nurses are on duty in the afternoon, even less during the night. Consequently, a 1 arXiv:2202.08895v1 [stat.AP] 4 Feb 2022 full time nurse works the most hours when the most deaths occur. The death rate is higher when she is present than when she is absent.

format_quoteCourt acquitted Daniela Poggiali of murder charges, attributing patient deaths to natural causes, indicating flaws in prosecution's case.format_quote

Submitted to the Statistical Science Statistics, Causality and Bell’s Theorem

Abstract. Bell’s (1964) theorem is popularly supposed to establish the non-locality of quantum ph... more Abstract. Bell’s (1964) theorem is popularly supposed to establish the non-locality of quantum physics. Violation of Bell’s inequality in experiments such as that of Aspect et al. (1982) provides empirical proof of non-locality in the real world. This paper reviews recent work on Bell’s theorem, linking it to issues in causality as understood by statisticians. The paper starts with a proof of a strong, finite sample, version of Bell’s inequality and thereby also of Bell’s theorem, which states that quantum theory is incompatible with the conjunction of three formerly uncontroversial physical principles, here referred to as locality, realism, and freedom. Locality is the principle that the direction of causality matches the di-rection of time, and that causal influences need time to propagate spa-tially. Realism and freedom are directly connected to statistical thinking on causality: they relate to counterfactual reasoning, and to randomisa-tion, respectively. Experimental loopholes ...

This is page Printer Opaque this Sequential models for coarsening and missingness

In a companion paper we described what intuitively would seem to be the most general possible way... more In a companion paper we described what intuitively would seem to be the most general possible way to generate Coarsening at Random mechanisms a sequential procedure called randomized monotone coarsen ing Counterexamples showed that CAR mechanisms exist which cannot be represented in this way Here we further develop these results in two directions Firstly we consider what happens when data is coarsened at random in two or more phases We show that the resulting coarsening mech anism is not CAR anymore but under suitable assumptions is identied and can provide interesting alternative analysis of data under a nonCAR model Secondly we look at sequential mechanisms for generating MAR data missing components of a multivariate random vector Randomised monotone missingness schemes in which one variable at a time is observed and depending on its value another variable is chosen or the procedure is terminated supply in our opinion the broadest class of physically in terpretable MAR mechanisms ...

Pearle’s Hidden-Variable Model Revisited

Entropy, 2019

Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the sing... more Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the singlet correlations of quantum theory, through the device of data-rejection: particles can fail to be detected in a way which depends on the hidden variables carried by the particles and on the measurement settings. If the experimenter computes correlations between measurement outcomes of particle pairs for which both particles are detected, he or she is actually looking at a subsample of particle pairs, determined by interaction involving both measurement settings and the hidden variables carried in the particles. We correct a mistake in Pearle’s formulas (a normalization error) and more importantly show that the model is simpler than first appears. We illustrate with visualizations of the model and with a small simulation experiment, with code in the statistical programming language R included in the paper. Open problems are discussed.

Censoring, truncation and filtering in statistical models based on counting processes

Contemporary Mathematics, 1988

The Centre for Mathematics and Computer Science is a research institute of the Stichting Mathemat... more The Centre for Mathematics and Computer Science is a research institute of the Stichting Mathematisch Centrum. which was founded on February 11 , 1946, as a nonprofit institution aiming at the promotion of mathematics. computer science, and their applications. It is sponsored by the Dutch Government through the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).