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Richard D. Gill

Publications and source records attributed to Richard D. Gill.

At least 37 records · Page 2Linked to original sources
arXiv2022

Relationship between incidence of breathing obstruction and degree of muzzle shortness in pedigree dogs

There has been much concern about health issues associated with the breeding of short-muzzled pedigree dogs. The Dutch government commissioned a scientific report \emph{Fokken met Kortsnuitige Honden} (Breeding of short muzzled dogs), van Hagen (2019), and based on it rather stringent legislation, restricting breeding primarily on the basis of a single simple measurement of brachycephaly, the CFR: cranial-facial ratio. Van Hagen's work is a literature study and it draws heavily on statistical results obtained in three publications: Njikam (2009), Packer et al.~(2015), and Liu et al.~(2017). In this paper I discuss some serious shortcomings of those three studies and in particular show that Packer et al.\ have drawn unwarranted conclusions from their study. In fact, new analyses using their data leads to an entirely different conclusion.

stat.AP↗
arXiv2022

Statistical issues in Serial Killer Nurse cases

We study statistical aspects of the case of the British nurse Ben Geen, convicted of 2 counts of murder and 15 of grievous bodily harm following events at Horton General Hospital (in the town of Banbury, Oxfordshire, UK) during December 2013-February 2014. We draw attention to parallels with the cases of nurses Lucia de Berk (the Netherlands) and Daniela Poggiali (Italy), in both of which an initial conviction for multiple murders of patients was overturned after reopening of the case. We pay most attention to the investigative processes by which data, and not just statistical data, is generated; namely, the identification of past cases in which the nurse under suspicion might have been involved. We argue that the investigation and prosecution of such cases is vulnerable to many cognitive biases and errors of reasoning about uncertainty, complicated by the fact that fact-finders have to determine not only whether a particular person was guilty of certain crimes, but whether any crimes were committed by anybody at all. The paper includes some new statistical findings on the Ben Geen case and suggests further avenues for investigation. The experiences recounted here have contributed to the writing of the hand-book Green et al. (2022), Healthcare Serial Killer or Coincidence? Statistical Issues in Investigation of Suspected Medical Misconduct, commissioned by the Royal Statistical Society, Statistics and the Law section. Submitted to MDPI Laws. This version: 5 August, 2022.

stat.OT↗
arXiv2022

Teleportation into Quantum Statistics

The paper is a tutorial introduction to quantum information theory, developing the basic model and emphasizing the role of statistics and probability.

math.ST↗
arXiv2022

A solution for the rare type match problem when using the DIP-STR marker system

The rare type match problem is an evaluative challenging situation in which the analysis of a DNA profile reveals the presence of (at least) one allele which is not contained in the reference database. This situation is challenging because an estimate for the frequency of occurrence of the profile in a given population needs sophisticated evaluative procedures. The rare type match problem is very common when the DIP-STR marker system, which has proven itself very useful for dealing with unbalanced DNA mixtures, is used, essentially due to the limited size of the available database. The object-oriented Bayesian network proposed in Cereda, Biedermann, Hall and Taroni (2014) to assess the value of the evidence for general scenarios, was not designed to deal with this particular situation. In this paper, the model is extended and partially modified to be able to calculate the full Bayesian likelihood ratio in presence of any (observed and not yet observed) allele of a given profile. The method is based on the approach developed in Cereda (2017) for Y-STR data. Alternative solutions, such as the plug-in approximation and an empirical Bayesian methodology are also proposed and compared with the results obtained with the full Bayesian approach.

stat.AP↗
arXiv2022

No probability loophole in the CHSH

Geurdes (2014, Results in Physics) outlines a probabilistic construction of a counterexample to Bell's theorem. He gives a procedure to repeatedly sample from a specially constructed "pool" of local hidden variable models (depending on a table of numerically calculated parameters) and select from the results one LHV model, determining a random value S of the usual CHSH combination of four (theoretical) correlation values. He claims Prob(|S| > 2) > 0. We expose a fatal flaw in the analysis: the procedure generates a non-local hidden variable model. To disprove this claim, Geurdes should program his procedure and generate random LHV's till he finds one violating the CHSH inequality.

quant-ph↗
arXiv2022

Comment on "Dr. Bertlmann's Socks in a Quaternionic World of Ambidextral Reality"

I point out critical errors in the paper "Dr. Bertlmann's Socks in a Quaternionic World of Ambidextral Reality" by Joy~Christian, published in IEEE Access. Christian's model does not generate the singlet correlations but in fact simply reproduces the Bertlmann effect. John Bell's friend and colleague Reinhold Bertlmann of CERN, in his younger days, always wore one pink and one blue sock, at random. The moment you saw his left foot, you knew what colour sock would be on his right foot. Action at a distance? As John Bell liked to explain, quantum entanglement cannot be explained away in such an easy way. Yet Christian's model assigns the two particles of the EPR-B experiment an equal and opposite spin at the source, the choice being determined by a fair coin toss. However they are measured, these spins are recovered. Christian's computer simulation works by not actually simulating his model at all but by almost directly tracing the negative cosine built into his computer algebra package. Bell's theorem has not been disproved. Debate as to what it means for the foundations of physics as well as for quantum information engineering (quantum communication, computation) is more lively today than ever before. Christian's paper, alas, does not contribute to the debate, but distracts from it. A possible role for Geometric Algebra is still wide open and deserves further investigation, informed by a proper understanding of the mathematical content of Bell's theorem.

physics.gen-ph↗
arXiv2022

Comment on "Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space"

I point out critical errors in the paper "Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space" by J. Christian, published in IEEE Access. Christian's paper in fact contains several conflicting models. None of them form counterexamples to Bell's theorem. Most of Christian's paper is devoted to a model based on the detection loophole due to Pearle (1970).

quant-ph↗
arXiv2022

A nonparametric Bayesian approach to the rare type match problem

The "rare type match problem" is the situation in which the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. The evaluation of this match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) is based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles, that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions, and discards the information about the names of the different DNA profiles. This fits very well the data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to a justified Empirical Bayes approach.

stat.AP↗
arXiv2022

Gull's theorem revisited

Steve Gull, in unpublished work available on his Cambridge University homepage, has outlined a proof of Bell's theorem using Fourier theory. Gull's philosophy is that Bell's theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell's work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob's computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull's proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables.

quant-ph↗
arXiv2021

Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked

In this note, I analyze the data generated by M. Fodje's (2013, 2014) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.

quant-ph↗
arXiv2021

Does Geometric Algebra provide a loophole to Bell's Theorem? (with corrections)

In 2007, and in a series of later papers, Joy Christian claimed to refute Bell's theorem, presenting an alleged local realistic model of the singlet correlations using techniques from Geometric Algebra (GA). Several authors published papers refuting his claims, and Christian's ideas did not gain acceptance. However, he recently succeeded in publishing yet more ambitious and complex versions of his theory in fairly mainstream journals. How could this be? The mathematics and logic of Bell's theorem is simple and transparent and has been intensely studied and debated for over 50 years. Christian claims to have a mathematical counterexample to a purely mathematical theorem. Each new version of Christian's model used new devices to circumvent Bell's theorem or depended on a new way to misunderstand Bell's work. These devices and misinterpretations are in common use by other Bell critics, so it useful to identify and name them. I hope that this paper can serve as a useful resource to those who need to evaluate new "disproofs of Bell's theorem". Christian's fundamental idea is simple and quite original: he gives a probabilistic interpretation of the fundamental GA equation a.b = (ab + ba)/2. After that, ambiguous notation and technical complexity allow sign errors to be hidden from sight, and new mathematical errors can be introduced.

quant-ph↗
arXiv2020

Modelling Competing Legal Arguments using Bayesian Model Comparison and Averaging

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and 'average' Bayesian models of legal arguments that have been built independently and with no attempt to make them consistent in terms of variables, causal assumptions or parametrisation. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational.

stat.AP↗
arXiv2020

Pearle's Hidden-Variable Model Revisited

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 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 more simple than first appears. We illustrate with visualisations 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.

quant-ph↗
arXiv2019

Elementary Statistics on Trial (the case of Lucia de Berk)

In the conviction of Lucia de Berk an important role was played by a simple hypergeometric model, used by the expert consulted by the court, which produced very small probabilities of occurrences of certain numbers of incidents. We want to draw attention to the fact that, if we take into account the variation among nurses in incidents they experience during their shifts, these probabilities can become considerably larger. This points to the danger of using an oversimplified discrete probability model in these circumstances.

stat.AP↗
arXiv2016

Estimating a probability mass function with unknown labels

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We prove strong consistency and derive the rates of convergence, for an extended model version of the estimator. We also study a sieved estimator for which similar consistency results are derived. Numerical computation of the sieved estimator is of great interest for practical problems, such as forensic DNA analysis, and we present a computational algorithm based on the stochastic approximation of the expectation maximisation algorithm. As an interesting byproduct of the numerical analyses we introduce an algorithm for bounded isotonic regression for which we also prove convergence.

math.ST↗
arXiv2015

Statistics, Causality and Bell's Theorem

Bell's [Physics 1 (1964) 195-200] theorem is popularly supposed to establish the nonlocality of quantum physics. Violation of Bell's inequality in experiments such as that of Aspect, Dalibard and Roger [Phys. Rev. Lett. 49 (1982) 1804-1807] provides empirical proof of nonlocality 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 direction of time, and that causal influences need time to propagate spatially. Realism and freedom are directly connected to statistical thinking on causality: they relate to counterfactual reasoning, and to randomisation, respectively. Experimental loopholes in state-of-the-art Bell type experiments are related to statistical issues of post-selection in observational studies, and the missing at random assumption. They can be avoided by properly matching the statistical analysis to the actual experimental design, instead of by making untestable assumptions of independence between observed and unobserved variables. Methodological and statistical issues in the design of quantum Randi challenges (QRC) are discussed. The paper argues that Bell's theorem (and its experimental confirmation) should lead us to relinquish not locality, but realism.

stat.AP↗