Friday, February 14, 2014

Improved icons for Bayesian and frequentist analysis

This post presents icons that attempt to capture the essence of Bayesian and frequentist analysis. There are four icons: Bayesian and frequentist approaches to decisions about null values, and Bayesian and frequentist approaches to parameter estimation. This post is an update of a previous post, motivated by many helpful comments from readers. For an explanation of what I mean by the "essence" of the approaches, and what I hope to achieve from this exercise, please see the previous post. Without further ado, the icons are presented below, first in a 2x2 grid, then one at a time with explanations in the captions.

Bayesian Frequentist
Null value

Bayesian null value assessment: The light-blue lines indicate the posterior distribution of credible lines. The dark-pink line marks the null value (zero slope). The null value falls far outside any credible value. [Added Feb 16, 2014: Of course, the full decision rule involves a ROPE around the null value. The ROPE is not displayed here, just to keep the icon uncluttered.]

Frequentist null value assessment: The dark-blue line marks the best fit. The dark-pink line marks the null hypothesis.The light-pink lines show the sampling distribution from the null hypothesis. The best fit falls far outside any null-sampled line.

Bayesian estimation: The light-blue lines indicate the posterior distribution of credible lines. There is an explicit distribution of credibilities (i.e., posterior probabilities) across possibilities (possible slopes etc.).

Frequentist estimation: The dark-blue line marks the best fit. The two dark-pink lines mark the limits of the confidence interval. The light-pink lines show the sampling distributions around each of the confidence-interval limits; notice that the best-fit line falls at the extreme of each sampling distribution. There is no distribution of probabilities across possibilities; there are only three point values: the best fit and the two CI limits.
Creative Commons license appended Feb 18, 2014, as suggested by reader comment:
Creative Commons License The four iconic images for Bayesian and frequentist data analysis by John K. Kruschke are licensed under a Creative Commons Attribution 4.0 International License. Based on a work at


  1. Hi John,
    This looks really nice. It very well demonstrates the two different conditional probabilities that Bayesians and frequentists rely on, especially in the "null value assessment" case. Great job!

  2. Thanks John - With each iteration they get better!

    Would you like to add some license to them, so that we know how to correctly use the icons?

    For example, with CC-BY everybody can use them, but must attribute them to you, and must indicate any changes made:

    Or, with CC0 - the freest license - your work would be in the public domain, which means that everybody can use, change, and distribute it.

  3. Thanks for the suggestion. I've added the generic CC license. First time I've considered that, so I'm happy to be informed about pros, cons, and options.