Wagenmakers, E.-J., Morey, R. D., & Lee, M. D. (2016). Bayesian benefits for the pragmatic researcher. Current Directions in Psychological Science, 25, 169-176.
Short, accessible paper arguing for the benefits of Bayesian inference using examples from popular culture. This should be the first paper you read – even if it’s just for the fun of it.
Etz, A., Gronau, Q. F., Dablander, F., Edelsbrunner, P. A., & Baribault, B. (accepted). How to become a Bayesian in eight easy steps: An annotated reading list. Psychological Bulletin & Review
Discusses eight articles on Bayesian inference, provides an overview of the literature and controversies more broadly, and “offers a starting point for understanding the core tenets of Bayesian analysis, while requiring a low level of time commitment”.
Sorensen, T., & Vasishth, S. (in press). Bayesian linear mixed models using Stan: A tutorial for psychologists, linguists, and cognitive scientists. Quantitative Methods for Psychology.
Great tutorial on how to write linear mixed models in Stan, taking away the magic that comes with tools such as lme4. The paper is also a prime example of reproducible research, as all materials are hosted on Github.
Nicenboim, B., & Vasishth, S. (2016). Statistical methods for linguistic research: Foundational Ideas-Part II. arXiv preprint arXiv:1602.00245
This introduction to Bayesian inference touches on several topics that are missing standard introductions for psychology, such as the influence of the prior on statistical inference, and model selection using cross-validation methods. The paper provides a good overview and further references for in-depth treatment.
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. (submitted). Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications
This is an interesting paper as it discusses five advantages of the Bayes factor – the Bayesian way of testing hypothesis –, but also responds to ten common criticisms of the former, acknowledging that the Bayes factor is contentious among statisticians.
Lee, M.D. (in press). Bayesian methods in cognitive modeling. The Stevens’ Handbook of Experimental Psychology and Cognitive Neuroscience, Fourth Edition.
This paper contextualizes Bayesian methods in cognitive psychology and introduces a worked example from psychophysics using the software JAGS. Especially interesting are the sections on the role of the prior, and prior predictive distributions. If you want to get a taste of Lee & Wagenmakers (2013; see below), we highly recommend this text.
Richard McElreath (2016) Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Chapman & Hall/CRC Press.
Has been described a “pedagogical masterpiece”, and indeed is a really cool book. If you are getting started with Bayesian statistics, this is the book to buy!
Lee, M. D., & Wagenmakers, E.-J. (2013). Bayesian modeling for cognitive science: A practical course. Cambridge University Press
Practical book on Bayesian cognitive modeling covering the basics of parameter estimation, model comparison, as well as several case studies, among other things, in signal detection theory, psychophysics, and decision making.
Kruschke, J. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press.
This was one of the first textbooks on Bayesian statistics written for psychologists. It introduces you from the ground-up, starting with an introduction to R and probability theory. Because of its great pedagogical approach, the poems that start each chapter, and overall structure of the content, we can recommend this book.
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2014). Bayesian data analysis (Vol. 2). Boca Raton, FL, USA: Chapman & Hall/CRC.
This is the Bayesian bible, and thus must be on this list. It requires a sound background in mathematical statistics.
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