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“Learn how to see. Realize that everything connects to everything else.”
~ Leonardo da Vinci (*1452;†1519)
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Sky ain't the limit!
A powerful & flexible methodological alternative to mindless orthodox (paralogistic)
statistical null hypothesis significance testing (NHST) based on the fallacious/invalid logic associated with p-values and fixed α-levels.
Bayesian à posteriori parameter estimation
via Markov chain Monte Carlo simulations

A critique of p-values
"Few researchers are aware that their own heroes rejected what they practice routinely. Awareness of the origins of the ritual and of its rejection could cause a virulent cognitive dissonance, in addition to dissonance with editors, reviewers, and dear colleagues. Suppression of conflicts and contradicting information is in the very nature of this social ritual.”
(Gigerenzer, 2004, p. 592)

Display R code & references
Associated R codeBayesian paramter estimation via Markov chain Monte Carlo methods
#clears all of R's memory
rm(list=ls())
# Get the functions loaded into R's working memory
# The function can also be downloaded from the following URL: # http://irrational-decisions.com/?page_id=1996
source("BEST.R")
#download data from server
dataexp2 <-
read.table("https://www.irrational-decisions.com/phd-thesis/dataexp2.txt",
header=TRUE, sep="", na.strings="NA", dec=".", strip.white=TRUE)
# Specify data as vectors
y1 = c(dataexp2$v00)
y2 = c(dataexp2$v01)
# Run the Bayesian analysis using the default broad priors described by Kruschke (2013)
mcmcChain = BESTmcmc( y1 , y2 , priorOnly=FALSE ,
numSavedSteps=12000 , thinSteps=1 , showMCMC=TRUE )
postInfo = BESTplot( y1 , y2 , mcmcChain , ROPEeff=c(-0.1,0.1) )

#The function “BEST.R” can be downloaded from the CRAN (Comprehensive R Archive Network) repository under https://cran.r-project.org/web/packages/BEST/index.html
Kruschke, J. K., & Liddell, T. M.. ( 2018). The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review, 25(1), 178–206.

Plain numerical DOI: 10.3758/s13423-016-1221-4
DOI URL
directSciHub download



9th International Quantum Interactions conference (QI15)
Switzerland, Filzbach 2015
Manipal University Jaipur
India 2016

In anthropology (and the social and behavioral sciences) the terms emic and etic refer to two different types of field research. Emic is a perspective from within the social group (from the perspective of the subject). Per contrast, etic refers to an outside-perspective (from the perspective of the observer). In my opinion both are complementary to each other (in the quantum-physical sense of complementarity; cf. bistable perception).

Psychophysics meets Quantum Cognition

This presentation focuses on the role of noncommutativity in visual/perceptual decision-making.
First, some historical background information is provided.
Then, the interrelated concepts of complementarity and superposition are briefly delineated and two paradigmatic visual illusions are demonstrated.
Next, several pertinent empirical results are discussed in the theoretical framework of quantum cognition.
Finally, the interdisciplinary scope of the topic will be adumbrated in the context of "cognitive innovation" (CogNovo).

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An animated semantic MindMap
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Elliptical insights:
Visualising data in 3-dimensional Cartesian space
Expand this overlay to display additional information
Alexander von Humboldt on geometrical cognitionAssociated R codeR package on CRAN'Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry
Whatever relates to extent and quantity may be represented by geometrical figures. Statistical projections which speak to the senses without fatiguing the mind, possess the advantage of fixing the attention on a great number of important facts. ~ Alexander von Humboldt (1811)
scatterplot3d(x, y=NULL, z=NULL, color=par("col"), pch=par("pch"),
    main=NULL, sub=NULL, xlim=NULL, ylim=NULL, zlim=NULL,
    xlab=NULL, ylab=NULL, zlab=NULL, scale.y=1, angle=40,
    axis=TRUE, tick.marks=TRUE, label.tick.marks=TRUE,
    x.ticklabs=NULL, y.ticklabs=NULL, z.ticklabs=NULL,
    y.margin.add=0, grid=TRUE, box=TRUE, lab=par("lab"),
    lab.z=mean(lab[1:2]), type="p", highlight.3d=FALSE,
    mar=c(5,3,4,3)+0.1, bg=par("bg"), col.axis=par("col.axis"),
    col.grid="grey", col.lab=par("col.lab"), 
    cex.symbols=par("cex"), cex.axis=0.8 * par("cex.axis"),
    cex.lab=par("cex.lab"), font.axis=par("font.axis"),
    font.lab=par("font.lab"), lty.axis=par("lty"),
    lty.grid=par("lty"), lty.hide=NULL, lty.hplot=par("lty"),
    log="", asp=NA, ...)
Friendly, M., Monette, G., & Fox, J.. ( 2013). Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry. Statistical Science

Plain numerical DOI: 10.1214/12-STS402
DOI URL
directSciHub download



The Möbius band is an extraordinary geometrical figure. The band is eponymously named after the German mathematician August Ferdinand Möbius who described it in 1885, contemporaneously with another German mathematician named Johann Benedict Listing. It is a so called ruled surface with only one side and one boundary and it possesses the mathematical property of non-orientability (viz., a non-orientable manifold). In fact, the Möbius band is the simplest possible non-orientable surface. A Gedankenexperiment is helpful to understand this property intuitively: Imagine walking on the surface of a giant Möbius band. If you would travel long enough you would end up at the very starting point of the journey, only mirror-reversed. This journey can be repeated - ad infinitum. I argue that the Möbius band provides a reasily accessible metaphor for dual-aspect monism, a theory which challenges the predominant view that mind & matter (i.e., psyche & physis) are two fundamentally different substances. More information can be found on my eponymous websites.

Science and Nonduality Conference
California, San Jose (Silicon Valley)
2016
सरस्वति नमस्तुभ्यं वरदे कामरूपिणि
Saraswati Namastubhyam Varade Kama Rupini
Visualisation of various MCMC convergence diagnostics for μ1

Trace plot: In order to examine the representativeness of the MCMC samples, we first visually examine the trajectory of the chains. The trace plot indicates convergence on θ, i.e., the trace plot appears to be stationary because its mean and variance are not changing as a function of time.

Shrink factor (Brooks-Gelman-Rubin statistic). Theoretically, the larger the number of iterations T, the closer 𝑅 should approximate 1 (as T → ∞, 𝑅→ 1).

Autocorrelation (effective sample size/EES)

The density plot entails the 95% HDI and it displays the numerical value of the Monte Carlo Standard Error (MCSE) of 0.000454. The Monte Carlo Error (MCSE) is the uncertainty which can be attributed to the fact that the number of simulation draws is always finite. In other words, it provides a quantitative index that represents the quality of parameter estimates. The MCSE package in R provides convenient tools for computing Monte Carlo standard errors and the effective sample size (Gelman et al., 2004).

Expand overlay
Associated R codeBayesian paramter estimation via Markov chain Monte Carlo methods
#clears all of R's memory
rm(list=ls())
# Get the functions loaded into R's working memory
# The function can also be downloaded from the following URL: # http://irrational-decisions.com/?page_id=1996
source("BEST.R")
#download data from server
dataexp2 <-
read.table("http://www.irrational-decisions.com/phd-thesis/dataexp2.txt",
header=TRUE, sep="", na.strings="NA", dec=".", strip.white=TRUE)
# Specify data as vectors
y1 = c(dataexp2$v00)
y2 = c(dataexp2$v01)
# Run the Bayesian analysis using the default broad priors described by Kruschke (2013)
mcmcChain = BESTmcmc( y1 , y2 , priorOnly=FALSE ,
numSavedSteps=12000 , thinSteps=1 , showMCMC=TRUE )
postInfo = BESTplot( y1 , y2 , mcmcChain , ROPEeff=c(-0.1,0.1) )

#The function “BEST.R” can be downloaded from the CRAN (Comprehensive R Archive Network) repository under https://cran.r-project.org/web/packages/BEST/index.html
Kruschke, J. K., & Liddell, T. M.. ( 2018). The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review, 25(1), 178–206.

Plain numerical DOI: 10.3758/s13423-016-1221-4
DOI URL
directSciHub download
Kruschke, J. K.. ( 2011). Bayesian Assessment of Null Values Via Parameter Estimation and Model Comparison. Perspectives on Psychological Science, 6(3), 299–312.

Plain numerical DOI: 10.1177/1745691611406925
DOI URL
directSciHub download






Accumulation of evidence in favor of H₁
Sequential Bayes Factor analysis depicting the flow of evidence for various priors as n accumulates over time.
Bayes Factor robustness check for various Cauchy priors
In this example the maximum Bayes Factor was obtained at r ≈ 0.28 (max BF₁₀ ≈ 12.56).
Bayes Factor analysis: Prior and posterior plot
For this pairwise comparison we obtain a Bayes Factor of BF₁₀ ≈ 9.12 indicating that the data are circa 9 times more likely under H1 than under H0, i.e., P(D│H₁) ≈ 9.12.
Model comparison using Bayes Factor analysis
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Associated R packageSoftware downloadFurther References
JASP is based on the ‘BayesFactor’ R package which can be downloaded from the following URL: https://cran.r-project.org/web/packages/BayesFactor/index.html
JASP is an open-source statistics program that is free, friendly, and flexible. Armed with an easy-to-use GUI, JASP allows both classical and Bayesian analyses. URL: https://jasp-stats.org
Wagenmakers, E. J., Love, J., Marsman, M., Jamil, T., Ly, A., Verhagen, J., … Morey, R. D.. ( 2018). Bayesian inference for psychology. Part II: Example applications with JASP. Psychonomic Bulletin and Review

Plain numerical DOI: 10.3758/s13423-017-1323-7
DOI URL
directSciHub download



This animation which was created using R provides an intuitive explanation of what a 95% confidence interval really means:

If we would repeat the exact same experiment 50 times, then 95 % of the time the 50 confidence intervals would contain the true mean.

Visualisations are a powerful aid to understanding statistics. This makes sense from an evolutionary point of view as abstract symbolic cognition is phylogenetically much more recent than visual reasoning.

Empirical research has shown that the vast majority The American Psychological Association recommend confidence intervals as the "new statistics" in order to counteract the problems associuated with p-values. However, research clearly shows that confidence intervals are also widely misunderstood and they are therefore no real solution to the statistical croiis.
Out of 118 researcher only 3% were able to give the correct answer.
http://www.ejwagenmakers.com/inpress/HoekstraEtAlPBR.pdf

Visualising and understanding confidence intervals
Expand overlay
Associated R codeBayesian paramter estimation via Markov chain Monte Carlo methods
> library(animation)
> conf.int
function (level = 0.95, size = 50, cl = c("red", "gray"), ...) 
{
    n = ani.options("nmax")
    d = replicate(n, rnorm(size))
    m = colMeans(d)
....
Empirical research has shown that confidence are widely misunderstood. As with p-values most professional researchers do not understand the logic behind confidence intervals and their misinterpretation is a robust finding.
Hoekstra, R., Morey, R. D., Rouder, J. N., & Wagenmakers, E.-J.. ( 2014). Robust misinterpretation of confidence intervals. Psychonomic Bulletin & Review, 21(5), 1157–1164.

Plain numerical DOI: 10.3758/s13423-013-0572-3
DOI URL
directSciHub download
The animate package in R is a great way to visualise and understand the logic behind confidence intervals intuitively. The idea behind this simulation is simple: draw samples (random numbers) from the population which follows N(0, 1), and calculate confidence intervals (CI) based on these samples respectively.



Thesis abstract
Quantum cognition is an interdisciplinary emerging field within the cognitive sciences which applies various axioms of quantum mechanics to cognitive processes. This thesis reports the results of several empirical investigations which focus on the applicability of quantum cognition to psychophysical perceptual processes. Specifically, we experimentally tested several a priori hypotheses concerning 1) constructive measurement effects in sequential perceptual judgments and 2) noncommutativity in the measurement of psychophysical observables. In order to establish the generalisability of our findings, we evaluated our prediction across different sensory modalities (i.e., visual versus auditory perception) and in cross-cultural populations (United Kingdom and India). Given the well-documented acute “statistical crisis” in science (Loken & Gelman, 2017) and the various paralogisms associated with Fisherian/Neyman-Pearsonian null hypothesis significance testing, we contrasted various alternative statistical approaches which are based on complementary inferential frameworks (i.e., classical null hypothesis significance testing, nonparametric bootstrapping, model comparison based on Bayes Factors analysis, Bayesian bootstrapping, and Bayesian parameter estimation via Markov chain Monte Carlo simulations). This multimethod approach enabled us to analytically cross-validate our experimental results, thereby increasing the robustness and reliability of our inferential conclusions. The findings are discussed in an interdisciplinary context which synthesises knowledge from several prima facie separate disciplines (i.e., psychology, quantum physics, neuroscience, and philosophy). We propose a radical reconceptualization of various epistemological and ontological assumptions which are ubiquitously taken for granted (e.g., naïve and local realism/cognitive determinism). Our conclusions are motivated by recent cutting-edge findings in experimental quantum physics which are incompatible with the materialistic/deterministic metaphysical Weltanschauung internalised by the majority of scientists. Consequently, we argue that scientists need to update their nonevidence-based implicit beliefs in the light of this epistemologically challenging empirical evidence.

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In anthropology, folkloristics, and the social and behavioral sciences, emic and etic refer to two kinds of field research done and viewpoints obtained: emic, from within the social group (from the perspective of the subject) and etic, from outside (from the perspective of the observer).
Habitus & Hexis

This is my "steel tongue drum" (a beautiful handmade percussion instrument). It creates amazing sounds (the harmonic scale is D-minor consisting of the pitches 𝄞 D, E, F, G, A, B♭). The tonality deeply penetrates the mind. Listen to it for yourself and enjoy the vibrations... 🎜

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I took this picture in 2016 in Plymouth, English Garden, Mount Edgcumbe.

is virtually transformed by a "psychedelically inspired" Bayesian computer algorithm.
A magnificant flower
DeepDream is a "creative" computer algorithm developed by Google. According to the developers it is "psychedelically inspired".

I created this website because cognitive liberty (freedom of thought) is a fundamental human right which is currently under heavy attack. The website focuses on neuropolitics, history, social psychology, and cognitive psychology, inter alia.

Blue Room ~
Jaipur, India

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The word psyche is etymologically derived from the ancient Greek ψυχή (psukhḗ, which translates into “mind/soul/spirit/breath”). The suffix "logia" (λογία) can be translated as "the study of" (cf. lógos/λόγος which can be be translated, inter alia, as "subject matter Hence, psychology literally means "the study of mind/soul/spirit/breath”. However, many psychologists are utterly nescient of this etymological definition and are not very comfortable with these profound philosophical concepts. There are some laudable exceptions, for instance, the Swiss depth-psychologist C.G. Jung who wrote extensively on Indian psychology and pranayama (viz., psycho-spiritual breathing-exercises). Jung also coined the terms introversion/extroversion which are today widely utilised in mainstream psychology (the 5-factor model of personality). It should be noted that there is no science without philosophy!The notion that science can be seperated from philosophy is a naïve positivistic illusion which completly neglects the history of science. Until quite recently science was philosophy. The terminological dichotomisation is a modern invention.

Daniel Dennett formulated the following concise statement: “There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination."

— Daniel Dennett, Darwin's Dangerous Idea, 1995

Sanskrit etymology:
nata = actor, dancer, mime
raja = king
asana = posture, seat

Nataraja is another name for Shiva and his dance symbolizes cosmic energy. It is a challenging balancing asana (cerebellum) which trains focus and concentration (self-control/prefrontal executive functions). It is an extroverted asana full of creative energy.

Natarajasana - Lord of the Dance Pose
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As a net is made up by a series of knots, so everything in this world is connected by a series of knots. If anyone thinks that the mesh of a net is an independent, isolated thing, he is mistaken. […] and each mesh has its place and responsibilities in relation to other meshes.
~ Buddha

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The primary focus of this website is on psychology, neuroscience, consciousness & related subjects. An interdisciplinary approach is adopted according to the integral (viz., holarchical) scientific principle of epistemological holism.


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