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Richard D. Gill

Publications and source records attributed to Richard D. Gill.

At least 19 recordsLinked to original sources
arXiv2026

Critique of "Use of roster charts in the investigation and prosecution of nurses ..." by John O' Quigley

The paper "Use of roster charts in the investigation and prosecution of nurses suspected of inflicting deliberate harm on patients" by Prof. John O'Quigley explores an interesting hypothesis concerning statistical information hidden in the part of the infamous Lucy Letby roster chart pertaining to the 37 other nurses. Unfortunately, we have to point out some serious errors in his statistical analyses. The data actually contains information which strongly disproves his main modelling assumption. We do, however, strongly agree with him that from a forensic statistical point of view, the roster chart is fake evidence which should not have been shown to jurors.

stat.AP↗
arXiv2026

There to care; not to kill: medical settings, statistics and wrongful convictions

This paper discusses wrongful convictions in a medical setting, focusing on nurses. Common features are lack of strong direct evidence: the nurse was never seen doing anything wrong. There is no DNA evidence of tampering of apparatus or medications by the nurse. There is no CCTV footage showing suspicious actions. Analysis of medical records at the time led coroners to issue certificates of natural deaths, and most events were not, at the time, thought suspicious by hospital staff. There is no confession and the nurse consistently asserts they are completely innocent. There is no evidence of earlier psychopathic behaviour. Instead, private writings (e.g., in a diary) are interpreted by the prosecution as a confession; mundane behaviour is given a sinister interpretation. Motive remains speculation. The main evidence is statistical: a spike in deaths or collapses and a statistical association with a particular nurse. There is forensic evidence which suggests one or two patients might have been harmed by administration of medication much used in the hospital, and even legitimately used earlier in the care of the alleged victims. Police investigations are driven by the hospital consultants who were clinically responsible for the patients allegedly killed or harmed by the nurse.

stat.AP↗
arXiv2023

Kupczynski's Contextual Locally Causal Probabilistic Models are constrained by Bell's theorem

In a sequence of papers, Marian Kupczynski has argued that Bell's theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi's concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell-CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski's claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell-CHSH inequality is violated, so despite any other possible imperfections of such experiments, Kupczynski's escape route for local realism is not available

quant-ph↗
arXiv2023

Pitfalls of amateur regression: The Dutch New Herring controversies

Applying simple linear regression models, an economist analysed a published dataset from an influential annual ranking in 2016 and 2017 of consumer outlets for Dutch New Herring and concluded that the ranking was manipulated. His finding was promoted by his university in national and international media, and this led to public outrage and ensuing discontinuation of the survey. We reconstitute the dataset, correcting errors and exposing features already important in a descriptive analysis of the data. The economist has continued his investigations, and in a follow-up publication repeats the same accusations. We point out errors in his reasoning and show that alleged evidence for deliberate manipulation of the ranking could easily be an artefact of specification errors. Temporal and spatial factors are both important and complex, and their effects cannot be captured using simple models, given the small sample sizes and many factors determining perceived taste of a food product.

stat.AP↗
arXiv2023

Further comments on "Is the moon there if nobody looks? Bell inequalities and physical reality"

Kupczynski (2023) claims that Gill and Lambare (2022a, 2022b) misrepresent several of his published papers. This paper shows that the latest version of his "contextuality by default" model of a Bell experiment places no constraints whatsoever on the statistics of observed results in Bell type experiments. It thereby effectively allows arbitrary non-locality, ie direct causal effects of local measurement settings on distant measurement outcomes.

quant-ph↗
arXiv2023

Optimal statistical analyses of Bell experiments

We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell's S or Eberhard's J. Further improvement is obtained by using Wilks' likelihood ratio test based on the four tetranomially distributed vectors of counts of the four different outcome combinations, one 4-vector for each of the four setting combinations. The methodology is illustrated by application to the loophole-free Bell experiments of 2015 and 2016 performed in Delft and Munich, at NIST, and in Vienna respectively; and also to the earlier Innsbruck experiment of Weihs et al. (1998) and the recent Munich experiment of Zhang et al. (2022), which investigates use of a loophole-free Bell experiment as part of a protocol for Device Independent Quantum Key Distribution, DIQKD.

quant-ph↗
arXiv2023

Macroscopic Unobservability of Spinorial Sign Changes

In Section 5 of Christian (2014), published in IJTP, an experiment is described which is purported to have the capacity for exhibiting quantum correlations in a completely classical environment. Unfortunately the experiment has an interesting self-destructive property: it is certain not to deliver the required result, hence it is pretty certain that no experimenter will ever bother to perform it.

quant-ph↗
arXiv2023

The Monty Hall Problem is not a Probability Puzzle (it's a challenge in mathematical modelling)

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.

math.HO↗
arXiv2023

Conciliation of Bayes and Pointwise Quantum State Estimation: Asymptotic information bounds in quantum statistics

We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of the resulting data. The bound is an integrated version of a quantum Cramér-Rao bound due to Holevo (1982), and it thereby links the fixed N exact Bayesian optimality usually pursued in the physics literature with the pointwise asymptotic optimality favoured in classical mathematical statistics. By heuristic arguments the bound can be expected to be sharp. This does turn out to be the case in various important examples, where it can be used to prove asymptotic optimality of interesting and useful measurement-and-estimation schemes. On the way we obtain a new family of "dual Holevo bounds" of independent interest.

math.ST↗
arXiv2023

On Asymptotic Quantum Statistical Inference

We study asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam's theory of Local Asymptotic Normality.

quant-ph↗
arXiv2023

Comment on: Bell tests explained by classical optics without quantum entanglement

In a paper published in the journal Physics Essays in 2021, the author D.L. Mamas writes "A polarized photon interacts with a polarizer through the component of the photon's electric field which is aligned with the polarizer. This component varies as the cosine of the angle through which the polarizer is rotated, explaining the cosine observed in Bell test data. Quantum mechanics is unnecessary and plays no role". Mamas is right that according to this physical model, one will observe a negative cosine. However, the amplitude of the cosine curve is 50%, not 100%, and it consequently does not violate any Bell-CHSH inequality. Mamas' physical model is a classic local hidden variables model. The result is illustrated with a Monte Carlo simulation.

quant-ph↗
arXiv2023

Bell's theorem is an exercise in the statistical theory of causality

In this short note, I derive the Bell-CHSH inequalities as an elementary result in the present-day theory of statistical causality based on graphical models or Bayes' nets, defined in terms of DAGs (Directed Acyclic Graphs) representing direct statistical causal influences between a number of observed and unobserved random variables. I show how spatio-temporal constraints in loophole-free Bell experiments, and natural classical statistical causality considerations, lead to Bell's notion of local hidden variables, and thence to the CHSH inequalities. The word "local" applies to the way that the chosen settings influence the observed outcomes. The case of contextual setting-dependent hidden variables (thought of as being located in the measurement devices and dependent on the measurement settings) is automatically covered, despite recent claims that Bell's conclusions can be circumvented in this way.

quant-ph↗
arXiv2023

Commentary: Is the moon there if nobody looks -- Bell inequalities and physical reality

Marian Kupczynski(MK)is the author of a controversial paper published (2020) in the journal Frontiers in Physics. The work is built around a mathematical claim by MK which is actually false, and MK's logical reasoning around his claim is also incorrect. The same claim was made by him in several other recent papers published in other journals. A proof that the claimed result is false is the main content of our present "Comment". It is purely a mathematical counter-example to a mathematical claim in a number of MK's papers.

quant-ph↗
arXiv2022

History of applications of martingales in survival analysis

The paper traces the development of the use of martingale methods in survival analysis from the mid 1970's to the early 1990's. This development was initiated by Aalen's Berkeley PhD-thesis in 1975, progressed through the work on estimation of Markov transition probabilities, non-parametric tests and Cox's regression model in the late 1970's and early 1980's, and it was consolidated in the early 1990's with the publication of the monographs by Fleming and Harrington (1991) and Andersen, Borgan, Gill and Keiding (1993). The development was made possible by an unusually fast technology transfer of pure mathematical concepts, primarily from French probability, into practical biostatistical methodology, and we attempt to outline some of the personal relationships that helped this happen. We also point out that survival analysis was ready for this development since the martingale ideas inherent in the deep understanding of temporal development so intrinsic to the French theory of processes were already quite close to the surface in survival analysis.

stat.ME↗
arXiv2022

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 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 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.

stat.AP↗
arXiv2022

The triangle wave versus the cosine: How classical systems can optimally approximate EPR-B correlations

The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind consists of a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note, I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained "for free": they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a "spinning coloured disk" model, and a research programme: describe these functions in a concise analytic way. We survey open problems, and we show that the widespread idea that "quantum correlations are more extreme than classical physics allows" is at best highly inaccurate, through giving a concrete example of a classical correlation which satisfies all the symmetries and all the certainty relations and which exceeds the quantum correlations over a whole range of settings

quant-ph↗
arXiv2022

Schrödinger's cat meets Occam's razor

We discuss V.P. Belavkin's (2007) approach to the Schrödinger cat problem and show its close relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman (1995). The purpose of the paper is to explain these ideas in the most simple possible context, namely: discrete time and separable Hilbert spaces, in order to make them accessible to those coming from the philosophy of science and not too happy with idiosyncratic notation and terminology and sophisticated mathematical tools. Conventional elementary mathematical descriptions of quantum mechanics take "measurement" to be a primitive concept. Paradoxes arise when we choose to consider smaller or larger systems as measurement devices in their own right, by making different and apparently arbitrary choices of location of the "Heisenberg cut". Various quantum interpretations have different resolutions of the paradox. In Belavkin's approach, the classical world around us does really exist, and it evolves stochastically and dynamically in time according to probability laws following from successive applications of the Born law. It is a collapse theory, and necessarily it is non-local. The quantum/classical distinction is determined by the arrow of time. The underlying unitary evolution of the wave-function of the universe enables the designation of a collection of beables which grows as time evolves, and which therefore can be assigned random, classical trajectories. In a slogan: the past is particles, the future is a wave. We, living in the now, are located on the cutting edge between past and future.

quant-ph↗