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Richard D. Gill

Publications and source records attributed to Richard D. Gill.

51 records · Page 3Linked to original sources
arXiv2015

Time, Finite Statistics, and Bell's Fifth Position

I discuss three issues connected to Bell's theorem and Bell-CHSH-type experiments: time and the memory loophole, finite statistics (how wide are the error bars Under Local Realism), and the question of whether a loophole-free experiment is feasible, a surprising omission on Bell's list of four positions to hold in the light of his results. Levy's (1935) theory of martingales, and Fisher's (1935) theory of randomization in experimental design, take care of time and of finite statistics. I exploit a (classical) computer network metaphor for local realism to argue that Bell's conclusions are independent of how one likes to interpret probability, and give a critique of some recent anti-Bellist literature.

quant-ph↗
arXiv2014

Rarity of Respiratory Arrest in ED?

Statistical analysis of monthly rates of events in around 20 hospitals and over a period of about 10 years shows that respiratory arrest, though about five times less frequent than cardio-respiratory arrest, is a common occurrence in the Emergency Department of a typical smaller UK hospital. This report has been prepared at the request of lawyers working in the London Innocence Project and is intended to form part of an application to the CCRC for a reopening of the case of Ben Geen: a UK nurse sentenced to 30 years in jail following an apparent cluster of cases always when he was on duty at the Horton General Hospital.

stat.AP↗
arXiv2014

Forensic Statistics and Justice: the Leiden Consensus

Between 26 and 29 April 2011 a four-day interdisciplinary workshop "Science meets Law" was held at the Lorentz Center (University of Leiden, NL). It was organised by the Lorentz Center in collaboration with the Netherlands Institute for Advanced Study in the Humanities and Social Sciences ("NIAS", Wassenaar, NL). The programme was prepared by Richard Gill and Johannes F. Nijboer and connected to Richard Gill's 2010-2011 stay at NIAS as Distinguished Lorentz Fellow. This document was prepared by three of us and represents our personal synthesis of the discussions which took place during the meeting. Comments are welcome.

stat.AP↗
arXiv2013

Quantum local asymptotic normality based on a new quantum likelihood ratio

We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.

quant-ph↗
arXiv2010

The Three Doors Problem...-s

I argue that we must distinguish between: (0) the Three-Doors-Problem Problem [sic], which is to make sense of some real world question of a real person. (1) a large number of solutions to this meta-problem, i.e., many specific Three-Doors-Problem problems, which are competing mathematizations of the meta-problem (0). Each of the solutions at level (1) can well have a number of different solutions: nice ones and ugly ones; correct ones and incorrect ones. I discuss three level (1) solutions, i.e., three different Monty Hall problems; and try to give three short correct and attractive solutions. These are: an unconditional probability question; a conditional probability question; and a game-theory question. The meta-message of the article is that applied statisticians should beware of solution-driven science.

stat.AP↗
arXiv2009

Statistics, ethics, and probiotica

A randomized clinical trial comparing an experimental new treatment to a standard therapy for a life-threatening medical condition should be stopped early on ethical grounds, in either of the following scenarios: (1) it has become overwhelmingly clear that the new treatment is better than the standard; (2) it has become overwhelmingly clear that the trial is not going to show that the new treatment is any better than the standard. The trial is continued in the third scenario: (3) there is a reasonable chance that the new treatment will finally turn out to be better than the standard, but we aren't sure yet. However, the (blinded) data monitoring committee in the "PROPATRIA" trial of an experimental probiotica treatment for patients with acute pancreatitis allowed the trial to continue at the half way interim analysis, in effect because there was still a good chance of proving that the probiotica treatment was very harmful to their patients. The committee did not know whether treatment A was the probiotica treatment or the placebo. In itself this should not have caused a problem, since it could easily have determined the appropriate decision under both scenarios. Were the decisions in the two scenarios different, then the data would have to be de-blinded, in order to determine the appropriate decision. The committee mis-read the output of SPSS, which reports the smaller of two one-sided p-values, without informing the user what it is doing. It seems that about 5 lives were sacrificed to the chance of getting a significant result that the probiotica treatment was bad for the patients in the trial.

stat.AP↗
arXiv2008

An Algorithmic and a geometric characterization of coarsening at random

We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects generalizing the notion of partition of a set. However, the complexity of a given CAR mechanism can be large: the maximal "height" of the needed multicovers can be exponential in the number of points in the sample space. The results stem from a geometric interpretation of the set of CAR distributions as a convex polytope and a characterization of its extreme points. The hierarchy of CAR models defined in this way could be useful in parsimonious statistical modeling of CAR mechanisms, though the results also raise doubts in applied work as to the meaningfulness of the CAR assumption in its full generality.

math.ST↗
arXiv2007

Better Bell inequalities (passion at a distance)

I explain so-called quantum nonlocality experiments and discuss how to optimize them. Statistical tools from missing data maximum likelihood are crucial. New results are given on CGLMP, CH and ladder inequalities. Open problems are also discussed.

math.ST↗
arXiv2004

Asymptotics in Quantum Statistics

Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these parameters too, and statistical inference problems result. Often one has a choice of what measurement to take, corresponding to different experimental set-ups or settings of measurement apparatus. This leads to a design problem--which measurement is best for a given statistical problem. This paper gives an introduction to this field in the most simple of settings, that of estimating the state of a spin-half particle given n independent copies of the particle. We show how in some cases asymptotically optimal measurements can be constructed. Other cases present interesting open problems, connected to the fact that for some models, quantum Fisher information is in some sense non-additive. In physical terms, we have non-locality without entanglement.

math.ST↗
arXiv2004

On an Argument of David Deutsch

We analyse an argument of Deutsch, which purports to show that the deterministic part of classical quantum theory together with deterministic axioms of classical decision theory, together imply that a rational decision maker behaves as if the probabilistic part of quantum theory (Born's law) is true. We uncover two missing assumptions in the argument, and show that the argument also works for an instrumentalist who is prepared to accept that the outcome of a quantum measurement is random in the frequentist sense: Born's law is a consequence of functional and unitary invariance principles belonging to the deterministic part of quantum mechanics. Unfortunately, it turns out that after the necessary corrections we have done no more than give an easier proof of Gleason's theorem under stronger assumptions. However, for some special cases the proof method gives positive results while using different assumptions to Gleason. This leads to the conjecture that the proof could be improved to give the same conclusion as Gleason under unitary invariance together with a much weaker functional invariance condition.

quant-ph↗
arXiv2004

The chaotic chameleon

Various local hidden variables models for the singlet correlations exploit the detection loophole, or other loopholes connected with post-selection on coincident arrival times. I consider the connection with a probabilistic simulation technique called rejection-sampling, and pose some natural questions concerning what can be achieved and what cannot be achieved with local (or distributed) rejection sampling. In particular a new and more serious loophole, which we call the coincidence loophole, is introduced.

quant-ph↗
arXiv2003

A geometric proof of the Kochen-Specker no-go theorem

We give a short geometric proof of the Kochen-Specker no-go theorem for non-contextual hidden variables models. Note added to this version: I understand from Jan-Aake Larsson that the construction we give here actually contains the original Kochen-Specker construction as well as many others (Bell, Conway and Kochen, Schuette, perhaps also Peres).

quant-ph↗
arXiv2002

Accardi contra Bell (cum mundi): The Impossible Coupling

An experimentally observed violation of Bell's inequality is supposed to show the failure of local realism to deal with quantum reality. However, finite statistics and the time sequential nature of real experiments still allow a loophole for local realism, known as the memory loophole. We show that the randomized design of the Aspect experiment closes this loophole. Our main tool is van de Geer's (2000) supermartingale version of the classical Bernstein (1924) inequality guaranteeing, at the root n scale, a not-heavier-than-Gaussian tail of the distribution of a sum of bounded supermartingale differences. The results are used to specify a protocol for a public bet between the author and L. Accardi, who in recent papers (Accardi and Regoli, 2000a,b, 2001; Accardi, Imafuku and Regoli, 2002) has claimed to have produced a suite of computer programmes, to be run on a network of computers, which will simulate a violation of Bell's inequalites. At a sample size of thirty thousand, both error probabilities are guaranteed smaller than one in a million, provided we adhere to the sequential randomized design. The results also show that Hess and Philipp's (2001a,b) recent claims are mistaken that Bell's theorem fails because of time phenomena supposedly neglected by Bell.

quant-ph↗