Richard David Gill

Fengnan Gao and Richard D. Gill gut and de-bone the questionable statistics that destroyed a long-running culinary tradition

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.

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 was obtained by using the 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 was 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 (1998) Innsbruck experiment of Weihs et al. and the recent (2022) Munich experiment of Zhang et al., which investigates the use of a loophole-free Bell experiment as part of a protocol for device-independent quantum key distribution (DIQKD).

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.

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.

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.

In a controversial paper recently published in this journal, Marian Kupczynski claims that Bell-CHSH inequalities cannot be derived for a classical probabilistic causal model of a typical Bell experiment. Such an experiment can be seen as built up of four separate components, one for each of the four different combinations of settings used in the experiment. In this "Comment" we show that his claim is false and his logical reasoning is incorrect.

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.

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