Me and Eric-Jan Wagenmakers just finished our special issue in the Journal of Mathematical Psychology on “Bayes Factors for Testing Hypotheses in Psychological Research: Practical Relevance and New Developments”. We are grateful to all the interesting contributions by Bayesian experts, such as Jim Berger, Christian Robert, and Jeff Rouder. The contributions can be categorized into the following three partly overlapping themes: new philosophical insights, methodological innovations, and practical applications. Below you can find an overview of all contributions.

**Philosophical insights**

- Mulder, J. & Wagenmakers, E.-J. “Editors’ introduction to the special issue “Bayes factors for testing hypotheses in psychological research: Practical relevance and new developments”.
- Morey, R. D., Romeijn, J.-W, & Rouder, J. “The philosophy of Bayes factors and the quantification of statistical evidence”.
- Ly, A., Verhagen, J., & Wagenmakers, E.-J. “Harold Jeffreys’s default Bayes factor hypothesis tests: Explanation, extension, and application in psychology”.
- Robert, C. P. “The expected demise of the Bayes factor” (response to Ly, Verhagen, & Wagenmakers).
- Chandramouli, S. H. & Shiffrin, R. M. “Extending Bayesian Induction” (response to Ly, Verhagen, & Wagenmakers).
- Ly, A., Verhagen, J. & Wagenmakers, E.-J. “An evaluation of alternative methods for testing hypotheses, from the perspective of Harold Jeffreys” (rejoinder by Ly, Verhagen, & Wagenmakers). This rejoinder is in its final stage; currently the authors are revising this piece based on some minor comments from my side.
- Shiffrin, R. M., Chandramouli, S. H., Grünwald, P. D. “Bayes factors, relations to minimum description length, and overlapping model classes”.
- Dienes, Z. “How Bayes factors change scientific practice”.

**Methodological innovations**

- Bayarri, M. J., Benjamin, D. J., Berger, J. O., & Sellke, T. M. “Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses”.
- Mulder, J. “Bayes factors for testing order-constrained hypotheses on correlations”.
- Davis-Stober, C., Morey, R. D., Gretton, M. &Heathcote, A. “Bayes factors for state-trace analysis”.
- Gu, X., Hoijtink, H., & Mulder, J. “Error probabilities in default Bayesian hypothesis testing”.
- Nathoo, F. S. & Masson, M. E. J. Bayesian alternatives to null-hypothesis significance testing for repeated-measures designs.
- Böing-Messing, F. & Mulder, J. Automatic Bayes factors for testing variances of two independent normal distributions.

**Practical applications**

- Verhagen, J., Levy, R., Millsap, R. E., & Fox, J. P. “Evaluating evidence for invariant items: A Bayes factor approach to testing measurement invariance”.
- Vanpaemel, W. Prototypes, exemplars and the response scaling parameter: A Bayes factor perspective.
- Turner, B., Sederberg, P., & McClelland, J. “Bayesian analysis of simulation-based models”.
- Wetzels, R., Dolan, C., Tutschkow, D. van der Sluis, S. Dutilh, G., & Wagenmakers, E.-J. “A Bayesian test for the hot hand phenomenon”.
- Kary, A., Taylor, R., & Donkin, C. “Using Bayes factors to test the predictions of models: A case study in visual working memory”.

All papers are available online.

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