## Saturday, February 22, 2014

### Bayesian Tests to Quantify the Result of a Replication Attempt

This manuscript looks like a nice use of Bayes factors to assess replication results. I have not read it yet in detail, but the idea sounds right on target. From the abstract:
To quantify replication outcomes we propose a novel Bayesian replication test that compares the adequacy of two competing hypotheses. The first hypothesis is that of the skeptic and holds that the effect is spurious; this is the null hypothesis that postulates a zero effect size, H0: δ = 0. The second hypothesis is that of the proponent and holds that the effect is consistent with the one found in the original study, an effect that can be quantified by a posterior distribution. Hence, the second hypothesis --the replication hypothesis-- is given by Hr : δ ~ "posterior distribution from original study".
Here is the link: Bayesian Tests to Quantify the Result of a Replication Attempt; Josine Verhagen and Eric-Jan Wagenmakers, University of Amsterdam.

## 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:
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.