## Recently Published

##### AdvancedDelft

I now further sharpen the results by estimating the 8 parameters of the multinomial (No-Signalling) model by maximum likelihood, and also estimating the 7 parameters of the submodel obtained by restriction to Local Realism.
Statistical testing is probably improved by using the Wilks minus two log likelihood ratio test (compared to the chi-squared distribution with one degree of freedom), instead of a Wald test based on an estimated parameter and estimated asymptotic variance.
There are some surprising differences! Physicists should learn some textbook small-data statistical theory especially if their sample sizes are big!

##### AdvancedVienna

I now further sharpen the results by estimating the 8 parameters of the multinomial (No-Signalling) model by maximum likelihood, and also estimating the 7 parameters of the submodel obtained by restriction to Local Realism.
Statistical testing is probably improved by using the Wilks minus two log likelihood ratio test (compared to the chi-squared distribution with one degree of freedom), instead of a Wald test based on an estimated parameter and estimated asymptotic variance.
There are some surprising differences! Physicists should learn some textbook small-data statistical theory especially if their sample sizes are big!

##### AdvancedNIST

I now further sharpen the results by estimating the 8 parameters of the multinomial (No-Signalling) model by maximum likelihood, and also estimating the 7 parameters of the submodel obtained by restriction to Local Realism.
Statistical testing is probably improved by using the Wilks minus two log likelihood ratio test (compared to the chi-squared distribution with one degree of freedom), instead of a Wald test based on an estimated parameter and estimated asymptotic variance.
There are some surprising differences! Physicists should learn some textbook small-data statistical theory especially if their sample sizes are big!

##### AdvancedMunich

##### OptimizedVienna

Comparison of CHSH and J for the Vienna experiment, together with optimally noise-reduced versions of both. Theory: 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

##### OptimizedNIST

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

##### OptimizedMunich

Comparison of CHSH and J for the Munich experiment, together with optimally noise-reduced versions of both. Theory: 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

##### OptimizedDelft

Comparison of CHSH and J for the Delft experiment, together with optimally noise-reduced versions of both. Theory: 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

##### chili

Plots belonging to (2015) correction note of Brummert Lennings & Warburton (2011)

##### delft

The Delft experiment - three different scenarios

##### joy1

Counting the number of accepted particle pairs in Joy Christian's http://rpubs.com/jjc/84238

##### pearle2

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.

##### minkwe

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.

##### epr-clocked-full

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)

##### epr-clocked-core

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.

##### Christian's latest attempt

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.

##### onion2

An attempt to save Christian's one page paper by applying Albert Jan's patch to the central bug.

##### tree2

More fun with trees, in order to help visualising the junction tree algorithm

##### tree.Rmg

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 ...

##### onion

Test of Joy Christian's "one page paper" model http://arxiv.org/pdf/1103.1879v1.pdf of the singlet correlations.

##### maikel

Investigation of convergence of an integral in Esty's proof of the asymptotic normality of the Good estimator.

##### MLE_SMLE_script

Figure 1.7 of Groeneboom and Jongbloed (Bangkok data)

##### compare4

Comparison of various CH variants, and CHSH, for Giustina et al (fixed grid of coincidence windows, width = 50 time stamp units)

##### compare3

Compute optimal test of local realism for Christensen et al. data

##### compare1

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

##### compare

Comparison of Clauser-Horne and CHSH on Christensen et al. data.

##### Christensen4

Analysis of Christensen experiment starting from Graft's data: step 4: CHSH

##### Christensen3

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

##### Christensen2

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

##### Christensen1

Analysis of Christensen et al. data from Graft's data. Step 1, reduction of the data to small binary files, one for each experiment.

##### Christensen0

Analysis of Christensen et al. data using Graft's data sets. Step 0. Preparations.

##### conversions

Yet more exercises with R graphical models programs

##### gRain

Some quick exercises with graphical models in R

##### network

More advanced exercises with R and graphical models

##### CHSHalt

Giustina et al again, fixed time-slots, this time of 980 ns instead of 1000 ns

##### CHSH

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"

##### CH

Getting the statistics out of the raw data of the Giustina et al. experiment

##### zipf

An illustration of the Zipf law and a new estimation method

##### spreadsheet

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

##### JustinLee3

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 ...

##### JustinLee2

See my RPubs document JustinLee. This is the same but with slightly different parameters. We get a bigger violation of CHSH but smaller efficiencies ...

##### JustinLee

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"

##### joy

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

Simulation of diversity data from genomics, and a conjecture

##### yoichi

Moving balls about

##### probplots

Notes on probability plots, quantile plots, QQ plots ... to be expanded with R illustrations

##### Uitleg

Uitleg over Hilal Moussa's code

##### ist130903

Course "Introduction to Statistics", some R illustrations from Rice chapter 8

##### contour2

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.

##### contour

Illustration of R base graphics function "contour"

##### boxmueller

Visualisation of Box-Müller transformation

##### Opinion

Working document - are respiratory arrests rare in the Emergency Department of a hospital like Horton General (Banbury, UK)? (cf. case of Ben Geen).

##### esb.R

Alternative vs. official ESB ranking of Dutch economists according to Abbring et al.

##### testFred.R

Test of Fred Diether III's submission to the Christian experiment data challenge

##### test.R

My test program applied to Christian's latest submission to my challenge

##### epr-clocked.R

Michel Fodje's "epr-clocked" coincidence loophole model, stripped down to essential core https://github.com/minkwe/epr-clocked

##### epr-simple.R

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

##### Coincidence.R

Test

##### Coincidence.R

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.

##### gistfile1.R

"lambder" 's "Zen of R" https://gist.github.com/lambder/2066588

##### Zen.R

Zen's surface plot of Joy's simulation

##### christian.R

Test of Christian's claim to 10 000 Euro. Result = fail. Please try again, Joy.

##### bet2.R

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.

##### wireframe.R

The quantum correlation surface and the points on it of a CHSH-style experiment. Angles in degrees, from 0 to 180.

##### bet.R

Draft protocol of final stage of bet with Joy Christian. The two data sets will be replaced by data sets generated in his experiment.

##### gRain.R

Dawid and Evett network

##### fred3.R

Illustration of Theorem 1 of my "Statistics, Causality and Bell's Theorem" (the spreadsheet theorem), http://arxiv.org/abs/1207.5103

##### QRC.R

The quantum Randi challenge (Vongehr, 2012, 2013, ...) http://arxiv.org/abs/1207.5294

##### pearle.R

Simulation of the Pearle (1970) local hidden variables model

##### EPRB2.R

Minkwe's implementation of Christian's model, 2-d, R implementation by R D Gill

##### zen.R

Zen's modification of Joy's Experiment, adapted from Richard Gill's code, with constant shifts

##### joychristian.R

Joy's Experiment, adapted from Richard Gill's code, with constant shifts

##### ChaoticUnsharpBall1.R

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

##### ChaoticUnsharpBall3.R

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.

##### ChaoticUnsharpBall2.R

Script to investigate different radii distributions for the chaotic ball model / Christian-Roth model

##### ChaoticUnsharpBall.R

New name, but just a higher resolution performance of the Christian-Roth model http://rpubs.com/chenopodium/joychristian

##### EPRB2minkwe.R

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.

##### jcs2opt.R

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!)

##### Gisin2opt.R

Gisin and Gisin model (unsymmetrized version, for speed)
http://arxiv.org/abs/quant-ph/9905018

##### jcs2.R

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.

##### jcs.R

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

##### EPRB3opt.R

Optimized simulation of Joy Christian's S^2 (R^3) model.

##### EPRB23big.R

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.

##### Gisin2.R

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.

##### S2uniform.R

Sampling and plotting uniform random points on the uniform sphere

##### Chantal2.R

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!

##### EPRB23.R

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.R

Chantal Roth's local hidden variables model

##### EPRB3.R

Minkwe's implementation of Christian's model, 3-D, writen in R by R D Gill

##### yhrd.R

Y-str raw profiles plot

##### breuer.R

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

##### insight.R

Simulation of a citation count model - ideas due to Peter Breuer

##### solution week 2.html

Advanced Statistical Computing course, assignment for week 2

##### myknit.html

My first knitr attempt