Comparison of CHSH and J for the Vienna experiment, together with optimally noise-reduced versions of both. Theory: https://pub.math.leidenuniv.nl/~gillrd/Peking/Peking_4.pdf In short: assume four multinomial samples, estimate covariance matrix of estimated relative frequencies, use sample deviations from no-signalling to optimally reduce the noise in the estimate of Bell's S or Eberhard's J
Comparison of CHSH and J for the NIST experiment, together with optimally noise-reduced versions of both. Theory: https://pub.math.leidenuniv.nl/~gillrd/Peking/Peking_4.pdf In short: assume four multinomial samples, estimate covariance matrix of estimated relative frequencies, use sample deviations from no-signalling to optimally reduce the noise in the estimate of Bell's S or Eberhard's J
Comparison of CHSH and J for the Munich experiment, together with optimally noise-reduced versions of both. Theory: https://pub.math.leidenuniv.nl/~gillrd/Peking/Peking_4.pdf In short: assume four multinomial samples, estimate covariance matrix of estimated relative frequencies, use sample deviations from no-signalling to optimally reduce the noise in the estimate of Bell's S or Eberhard's J
Comparison of CHSH and J for the Delft experiment, together with optimally noise-reduced versions of both. Theory: https://pub.math.leidenuniv.nl/~gillrd/Peking/Peking_4.pdf In short: assume four multinomial samples, estimate covariance matrix of estimated relative frequencies, use sample deviations from no-signalling to optimally reduce the noise in the estimate of Bell's S or Eberhard's J
Plots belonging to (2015) correction note of Brummert Lennings & Warburton (2011)
The Delft experiment - three different scenarios
Counting the number of accepted particle pairs in Joy Christian's http://rpubs.com/jjc/84238
A simulation of Pearle's (1970) model for the EPR-Bohm correlations. In this script, I want to show how particle pairs move in and out of the sample as we increase one of the measurement angles, keeping the other fixed. We start with alpha = beta = 0 degrees, then increment beta by steps of 1 degree, till we come full circle at beta = 360 degrees. The sample size is small (10^4) to make for a fast running script.
I analyse the data generated by M. Fodje's simulation programs "epr-simple" and "epr-clocked" using appropriate modified Bell-CHSH type inequalities: the Larsson detection loophole adjusted CHSH, and the Larsson-Gill coincidence loophole adjusted CHSH. The experimental efficiencies turn out to be approximately eta = 81% and gamma = 55% respectively, and the observed value of CHSH is (of course) well within the adjusted bounds.
Michel Fodje's "epr-clocked" now with all bells and whistles, together with verification that the simulation results do not violated the Larsson-Gill corrected CHSH inequality (corrected for coincidence post-selection)
Michel Fodje's "epr-clocked", core part of model, many different performance metrics. In particular, verification that the simulation results do not violate the Larsson-Gill (2004) corrected CHSH inequality - corrected for coincidence loophole post-selection.
Joy Christian's http://rpubs.com/jjc/84238; Two lines added in order to illustrate varying sample sizes. Nothing else changed. It would be interesting to also study the overlap between the different samples. I'm thinking about how to visualise that in a sensible way.
An attempt to save Christian's one page paper by applying Albert Jan's patch to the central bug.
More fun with trees, in order to help visualising the junction tree algorithm
Draw a random tree with two nodes and the path between them marked by different colours. Part of attempt to explain the junction tree algorithm ...
Test of Joy Christian's "one page paper" model http://arxiv.org/pdf/1103.1879v1.pdf of the singlet correlations.
Investigation of convergence of an integral in Esty's proof of the asymptotic normality of the Good estimator.
Figure 1.7 of Groeneboom and Jongbloed (Bangkok data)
Comparison of various CH variants, and CHSH, for Giustina et al (fixed grid of coincidence windows, width = 50 time stamp units)
Compute optimal test of local realism for Christensen et al. data
Comparison of statistical power of CHSH and CH in ideal experiment. Also, comparison of aggregate data from Christensen et al. paper and as recomputed by me
Comparison of Clauser-Horne and CHSH on Christensen et al. data.
Analysis of Christensen experiment starting from Graft's data: step 4: CHSH
Analysis of Christensen et al. experiment from Graft's data, step 3: computation of B and B' (normalized Clauser-Horne) for all 20 data-sets
Analysis of Christensen et al. experiment from Graft data. Step 2. Reduction to set of coincidence counts, singles counts, and empty window counts, for all 20 data-sets
Analysis of Christensen et al. data from Graft's data. Step 1, reduction of the data to small binary files, one for each experiment.
Analysis of Christensen et al. data using Graft's data sets. Step 0. Preparations.
Yet more exercises with R graphical models programs
Some quick exercises with graphical models in R
More advanced exercises with R and graphical models
Giustina et al again, fixed time-slots, this time of 980 ns instead of 1000 ns
Analysis of Giustina et al. data using fixed 1000 nanosecond time-slots and coarse-graining: the two outcomes are: "one of more events in time-slot"; "no events in time-slot"
Getting the statistics out of the raw data of the Giustina et al. experiment
An illustration of the Zipf law and a new estimation method
Generates a spreadsheet and random settings such that the Bell-CHSH inequality is resoundingly violated (and quantum mechanics prediction for the singlet state confirmed) at N = 800, http://arxiv.org/abs/1207.5103
See my RPubs documents JustinLee, and JustinLee2. This is the same as JustinLee2, zooming in to see more clearly the difference between the two correlation curves ...
See my RPubs document JustinLee. This is the same but with slightly different parameters. We get a bigger violation of CHSH but smaller efficiencies ...
A simulation of Justin Lee's (2014) precession model for the EPR-Bohm correlations http://vixra.org/abs/1408.0063 "Bell's Inequality Loophole: Precession"
Adaptation of Joy Christian's script http://rpubs.com/jjc/16415, now we just print out the four correlations for the four combinations of angles in a CHSH experiment. An error is corrected in http://rpubs.com/gill1109/80119
Simulation of diversity data from genomics, and a conjecture
Moving balls about
Notes on probability plots, quantile plots, QQ plots ... to be expanded with R illustrations
Uitleg over Hilal Moussa's code
Course "Introduction to Statistics", some R illustrations from Rice chapter 8
Here is an example of using the function “contour” from the base graphics package in R to draw a contour plot. This improves and extends a previous version.
Illustration of R base graphics function "contour"
Visualisation of Box-Müller transformation
Working document - are respiratory arrests rare in the Emergency Department of a hospital like Horton General (Banbury, UK)? (cf. case of Ben Geen).
Alternative vs. official ESB ranking of Dutch economists according to Abbring et al.
Test of Fred Diether III's submission to the Christian experiment data challenge
My test program applied to Christian's latest submission to my challenge
Michel Fodje's "epr-clocked" coincidence loophole model, stripped down to essential core https://github.com/minkwe/epr-clocked
Michel Fodje's epr-simple simulation of the singlet correlations, run under the protocol of a delayed choice, event-ready-detectors, Bell-CHSH type experiment
Simulation of the Larsson-Gill coincidence loophole model. Parameters chosen to exactly reproduce CHSH = 2 sqrt 2. Sample size N = 10^4. This sample coincidentally just violates the Larsson-Gill population bound, though not significantly, if we take standard errors into account and use a reasonable significance level.
"lambder" 's "Zen of R" https://gist.github.com/lambder/2066588
Zen's surface plot of Joy's simulation
Test of Christian's claim to 10 000 Euro. Result = fail. Please try again, Joy.
Version 2 of the code for deciding the bet between Christian and Gill, concerning the results of Christian's exploding ball experiment. This version: each correlation is based on a different sample, chosen at random, completely disjoint.
The quantum correlation surface and the points on it of a CHSH-style experiment. Angles in degrees, from 0 to 180.
Draft protocol of final stage of bet with Joy Christian. The two data sets will be replaced by data sets generated in his experiment.
Dawid and Evett network
Illustration of Theorem 1 of my "Statistics, Causality and Bell's Theorem" (the spreadsheet theorem), http://arxiv.org/abs/1207.5103
The quantum Randi challenge (Vongehr, 2012, 2013, ...) http://arxiv.org/abs/1207.5294
Simulation of the Pearle (1970) local hidden variables model
Minkwe's implementation of Christian's model, 2-d, R implementation by R D Gill
Zen's modification of Joy's Experiment, adapted from Richard Gill's code, with constant shifts
Joy's Experiment, adapted from Richard Gill's code, with constant shifts
Gill - Thompson model. Chaotic rotating ball model with circular caps with radius R = ( 1 + U^gamma) * 45 degrees, where gamma = 0.46 is a bit smaller than 1/2
Computational proof that we can achieve the cosine exactly in the Joy Christian - Michel Fodje - Chantal Roth / Caroline Thompson - Richard Gill simulation model ... a convex combination of the blue curves will give us the black curve.
Script to investigate different radii distributions for the chaotic ball model / Christian-Roth model
New name, but just a higher resolution performance of the Christian-Roth model http://rpubs.com/chenopodium/joychristian
Michel Fodje's model: theta_0 sampled from the discrete uniform on angles at steps of 7.5 degree between 0 and 90 degrees. To be precise: "0" included, "90" excluded in this code.
Port of Chantal Roth's simulation of Joy's model from Java to R This variant: optimised for speed, now 10^6 runs (optimisation is, of course, unfortunately at some cost to transparency!)
Gisin and Gisin model (unsymmetrized version, for speed) http://arxiv.org/abs/quant-ph/9905018
Port of Chantal Roth's simulation of Joy's model from Java to R. This variant: just one angle pair (alpha = beta = 0), but now 10^6 runs. The observed correlation is 0.98, not 1.
Port of Chantal Roth's simulation of Joy's model to R https://github.com/chenopodium/JCS https://github.com/chenopodium/JCS2 http://libertesphilosophica.info/eprsim/EPR_3-sphere_simulation5M.html http://libertesphilosophica.info/eprsim/eprsim.txt
Optimized simulation of Joy Christian's S^2 (R^3) model.
This is essentially the same script as my recent EPRB23.R. Comparison of two versions of Christian's/Minkwe's/Thompson's LHV models: S^1 (R^2) and S^2 (R^3). I only look at one angle but take the sample size equal to 100 million. 100 times larger than the previous, hence 10 times smaller standard error.
Gisin and Gisin EPR-B local hidden variables model: http://arxiv.org/abs/quant-ph/9905018 Generate 1 million particle pairs. Measure them in 20 random pairs of directions.
Sampling and plotting uniform random points on the uniform sphere
This is Chantal Roth's adaptation of my code of her model. Additional features: try different "fudge factors"; compute CHSH. Based on RDG's understanding of Chantal's java code at https://github.com/chenopodium/EPR This is still a "beta testing" version. Main missing feature: any explanation of what is going on!
Comparison of Michel Fodje's model 2D and 3D (S^1 and S^2) = Joy Christian's model = Caroline Thompson's model: "the chaotic spinning ball" (or disk) with random disk sphere cap radii.
Chantal Roth's local hidden variables model
Minkwe's implementation of Christian's model, 3-D, writen in R by R D Gill
Y-str raw profiles plot
This is another try at modelling citation data according to Peter Breuer's model. This time I take the plot seriously and take the fitted straight line literally as a probability model. I show that data simulated according to this model is approximately log normally distributed
Simulation of a citation count model - ideas due to Peter Breuer
Advanced Statistical Computing course, assignment for week 2
My first knitr attempt