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
assessment
Estimation

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 http://doingbayesiandataanalysis.blogspot.com/2014/02/improved-icons-for-bayesian-and.html.

3 comments:

  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!

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  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: http://creativecommons.org/licenses/by/4.0/

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

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  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.

    ReplyDelete