This post highlights a recent special issue on Bayesian inference edited by Joachim Vandekerckhove, Jeff Rouder, and John Kruschke for *Psychonomic Bulletin & Review*. What sets this special issue apart is that most of the 16 contributions (spanning a total of 285 pages!) have a tutorial character. Researchers and students who are new to Bayesian inference –its theoretical underpinnings, its advantages in practice, its application to concrete data analysis problems– could do worse than study this special issue cover to cover. Note: several contributions are open access; those behind a paywall may be easily obtained through Sci-Hub.

In their introduction, the editors describe the contents of the special issue as follows:

“The special issue is divided into four sections. The first section is a coordinated five-part introduction that starts from the most basic concepts and works up to the general structure of complex problems and to contemporary issues. The second section is a selection of advanced topics covered in-depth by some of the world’s leading experts on statistical inference in psychology. The third section is an extensive collection of teaching resources, reading lists, and strong arguments for the use of Bayesian methods at the expense of classical methods. The final section contains a number of applications of advanced Bayesian analyses that provide an idea of the wide reach of Bayesian methods for psychological science.”

### Personal Highlights

The special issue contains two papers by the JASP team, originally two parts of a single manuscript. The paper “Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications” contains a handy table that summarizes the advantages and disadvantages of Bayes inference compared to frequentist inference:

In “Part II: Example applications with JASP” we discuss how JASP can be used to execute Bayesian analyses for common analysis problems such as t-tests and ANOVAs. Here’s the first figure of that paper:

### How to Become a Bayesian in Eight Easy Steps

Almost every paper in this special issue deserves to be highlighted. For instance, there is the “meta-tutorial” by Alex Etz and others, “How to become a Bayesian in eight easy steps: An annotated reading list”. Etz et al. discuss a host of accessible articles and books on Bayesian inference. This is all the more important because the current literature resembles a veritable minefield, where titles such as “A Dumbed-Down-to-the-Ground Introduction to Bayesian Inference” may in fact require a solid mathematical background to be understood — such beguiling titles omit the intended audience: “…for Mathematical Statisticians”. And although there is nothing wrong with accessible introductions for mathematical statisticians, the main concepts of Bayesian inference are sufficiently simple that they can be appreciated without first immersing oneself in measurement theory. After all, at its core Bayesian inference is just a theory of learning, that is, “common sense expressed in numbers”. At any rate, a key figure of the Etz paper is the following:

When people ask me for accessible material on Bayesian inference, I always refer them to the Etz et al. paper.

### A Harry Potter Introduction to Bayesian Inference

While on the topic of accessible introductions, another Etz paper from the special issue deserves mention as well. In “Introduction to Bayesian inference for psychology”, Etz and Vandekerckhove present what is perhaps the single most attractive and compelling introduction to Bayesian thinking. The concrete data analysis problems are cast in terms of stories from the Harry Potter books. This is the start of their fourth example, “Of Murtlaps and Muggles”:

“According to

Fantastic Beasts and Where to Find Them(Scamander, 2001), a Murtlap is a “rat-like creature found in coastal areas of Britain” (p. 56). While typically not very aggressive, a startled Murtlap might bite a human, causing a mild rash, discomfort in the affected area, profuse sweating, and some more unusual symptoms. Anecdotal reports dating back to the 1920s indicate that Muggles (non-magical folk) suffer a stronger immunohistological reaction to Murtlap bites. This example of physiological differences between wizards and Muggles caught the interest of famed magizoologist Newton (“Newt”) Scamander, who decided to investigate the issue: When bitten by a Murtlap, do symptoms persist longer in the average Muggle than in the average wizard? The Ministry of Magic keeps meticulous historical records of encounters between wizards and magical creatures that go back over a thousand years, so Scamander has a great deal of information on wizard reactions to Murtlap bites. Specifically, the average duration of the ensuing sweating episode is 42 hours, with a standard deviation of 2. Due to the large amount of data available, the standard error of measurement is negligible. Scamander’s question can now be rephrased: What is the probability a Murtlap bite on a Muggle results in an average sweating episode longer than 42 hours?”

### Conclusion

The PBR special issue on Bayesian inference presents a series of 16 papers that are invaluable for researchers and students who wish to learn more about Bayesian reasoning and how it can facilitate their work. In future blog posts I hope to return to some of the other contributions to this special issue.

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Etz, A., Gronau, Q. F., Dablander, F., Edelsbrunner, P. A., & Baribault, B. (2018). How to become a Bayesian in eight easy steps: An annotated reading list. *Psychonomic Bulletin & Review, 25*, 219-234.

Etz, A., & Vandekerckhove, J. (2018). Introduction to Bayesian inference for psychology. *Psychonomic Bulletin & Review, 25*, 5-34. DOI 10.3758/s13423-017-1262-3

Scamander, N. A. F. (2001). *Fantastic beasts and where to find them*. London, UK: Obscurus Books.

Vandekerckhove, J., Rouder, J. N., & Kruschke, J. K. (2018). Editorial: Bayesian methods for advancing psychological science. *Psychonomic Bulletin & Review, 25*, 1-4.

Wagenmakers, E.-J., Marsman, M., Jamil, T., Ly, A., Verhagen, A. J., Love, J., Selker, R., Gronau, Q. F., Smira, M., Epskamp, S., Matzke, D., Rouder, J. N., & Morey, R. D. (2018a). Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications. *Psychonomic Bulletin & Review, 25*, 35-57. Open Access.

Wagenmakers, E.-J., Love, J., Marsman, M., Jamil, T., Ly, A., Verhagen, A. J., Selker, R., Gronau, Q. F., Dropmann, D., Boutin, B., Meerhoff, F., Knight, P., Raj, A., van Kesteren, E.-J., van Doorn, J., Smira, M., Epskamp, S., Etz, A., Matzke, D., de Jong, T., van den Bergh, D., Sarafoglou, A., Steingroever, H., Derks, K., Rouder, J. N., Morey, R. D. (2018b). Bayesian inference for psychology. Part II: Example applications with JASP. *Psychonomic Bulletin & Review, 25*, 58-76. Open Access.