# How to become a Bayesian in eight easy steps: An annotated reading list

## Abstract

In this guide, we present a reading list to serve as a concise introduction to Bayesian data analysis. The introduction is geared toward reviewers, editors, and interested researchers who are new to Bayesian statistics. We provide commentary for eight recommended sources, which together cover the theoretical and practical cornerstones of Bayesian statistics in psychology and related sciences. The resources are presented in an incremental order, starting with theoretical foundations and moving on to applied issues. In addition, we outline an additional 32 articles and books that can be consulted to gain background knowledge about various theoretical specifics and Bayesian approaches to frequently used models. Our goal is to offer researchers a starting point for understanding the core tenets of Bayesian analysis, while requiring a low level of time commitment. After consulting our guide, the reader should understand how and why Bayesian methods work, and feel able to evaluate their use in the behavioral and social sciences.

## Keywords

Bayesian statistics Hypothesis testing## Notes

### Acknowledgments

The authors would like to thank Jeff Rouder, E.-J. Wagenmakers, and Joachim Vandekerckhove for their helpful comments. AE and BB were supported by grant #1534472 from NSF’s Methods, Measurements, and Statistics panel. AE was further supported by the National Science Foundation Graduate Research Fellowship Program (#DGE1321846).

## References

- Aho, K., Derryberry, D., & Peterson, T. (2014). Model selection for ecologists: The worldviews of AIC and BIC.
*Ecology*,*95*(3), 631–636. doi: 10.1890/13-1452.1. Retrieved from http://tinyurl.com/aho2014.CrossRefPubMedGoogle Scholar - Bartlema, A., Voorspoels, W., Rutten, F., Tuerlinckx, F., & Vanpaemel, W. (this issue). Sensitivity to the prototype in children with high-functioning autism spectrum disorder: An example of Bayesian cognitive psychometrics.
*Psychonomic Bulletin and Review*.Google Scholar - Berger, J. O. (2006). The case for objective Bayesian analysis.
*Bayesian Analysis*,*1*(3), 385–402. doi: 10.1214/06-BA115. Retrieved from http://projecteuclid.org/euclid.ba/1340371035.CrossRefGoogle Scholar - Berger, J. O., & Berry, D. A. (1988). Statistical analysis and the illusion of objectivity.
*American Scientist*,*76*(2), 159–165. Retrieved from http://www.jstor.org/stable/27855070 Google Scholar - Berger, J. O., & Delampady, M. (1987). Testing precise hypotheses.
*Statistical Science*, 317–335. Retrieved from https://projecteuclid.org/euclid.ss/1177013238 - Cornfield, J. (1966). Sequential trials, sequential analysis, and the likelihood principle.
*The American Statistician*,*20*, 18–23. Retrieved from http://www.jstor.org/stable/2682711 Google Scholar - Cumming, G. (2014). The new statistics why and how.
*Psychological Science*,*25*(1), 7–29. doi: 10.1177/0956797613504966. Retrieved from http://pss.sagepub.com/content/25/1/7.CrossRefPubMedGoogle Scholar - DeGroot, M. H. (1982). Lindley’s paradox: Comment.
*Journal of the American Statistical Association*, 336–339. Retrieved from http://www.jstor.org/stable/2287246 - Dienes, Z (2008).
*Understanding psychology as a science: An introduction to scientific and statistical inference*. Palgrave Macmillan.Google Scholar - Dienes, Z. (2011). Bayesian versus orthodox statistics: Which side are you on?
*Perspectives on Psychological Science*,*6*(3), 274–290. Retrieved from http://tinyurl.com/dienes2011 CrossRefPubMedGoogle Scholar - Dienes, Z. (2014). Using Bayes to get the most out of nonsignificant results.
*Frontiers in Psychology*,*5*. Retrieved from http://journal.frontiersin.org/article/10.3389/fpsyg.2014.00781/full - Dienes, Z., & McLatchie, N. (this issue). Four reasons to prefer Bayesian over orthodox statistical analyses.
*Psychonomic Bulletin and Review*.Google Scholar - Dienes, Z., & Overgaard, M. (2015). How Bayesian statistics are needed to determine whether mental states are unconscious.
*Behavioural Methods in Consciousness Research*, 199–220. Retrieved from http://tinyurl.com/dienes2015 - Edwards, W., Lindman, H., & Savage, L. J. (1963). Bayesian statistical inference for psychology research.
*Psychological Review*,*70*(3), 193–242. Retrieved from http://tinyurl.com/edwards1963 CrossRefGoogle Scholar - Etz, A., & Vandekerckhove, J. (2016).
*PLOS ONE*,*11*, e0149794. Retrieved from http://dx.doi.org/10.1371%2Fjournal.pone.0149794. doi: 10.1371/journal.pone.0149794.CrossRefPubMedPubMedCentralGoogle Scholar - Etz, A., & Vandekerckhove, J. (this issue). Introduction to Bayesian inference for psychology.
*Psychonomic Bulletin and Review*.Google Scholar - Etz, A., & Wagenmakers, E.-J. (in press). J. B. S. Haldane’s contribution to the Bayes factor hypothesis test.
*Statistical Science*.Google Scholar - Franke, M. (2016). Task types, link functions & probabilistic modeling in experimental pragmatics. In F. Salfner & U. Sauerland (Eds.),
*Preproceedings of ‘trends in experimental pragmatics’*(pp. 56–63).Google Scholar - Gallistel, C. (2009). The importance of proving the null.
*Psychological Review*,*116*(2), 439. Retrieved from http://tinyurl.com/gallistel CrossRefPubMedPubMedCentralGoogle Scholar - Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D., Vehtari, A., & Rubin, D. B. (2013).
*Bayesian data analysis*(Vol. 3). Chapman & Hall/CRC.Google Scholar - Gelman, A., & Loken, E. (2014). The statistical crisis in science.
*American Scientist*,*102*(6), 460. Retrieved from http://tinyurl.com/gelman2014 CrossRefGoogle Scholar - Gelman, A., & Shalizi, C. R. (2013). Philosophy and the practice of Bayesian statistics.
*British Journal of Mathematical and Statistical Psychology*,*66*(1), 8–38. doi: 10.1111/j.2044-8317.2011.02037.x. Retrieved from http://tinyurl.com/gelman2013.CrossRefPubMedGoogle Scholar - Gigerenzer, G. (2004). Mindless statistics.
*The Journal of Socio-Economics*,*33*(5), 587–606. doi: 10.1016/j.socec.2004.09.033. Retrieved from http://tinyurl.com/gigerenzer2004.CrossRefGoogle Scholar - Goldstein, M., & et al. (2006). Subjective Bayesian analysis: Principles and practice.
*Bayesian Analysis*,*1*(3), 403–420. Retrieved from http://projecteuclid.org/euclid.ba/1340371036.CrossRefGoogle Scholar - Gronau, Q. F., Sarafoglou, A., Matzke, D., Ly, A., Boehm, U., Marsman, M., ..., & Steingroever, H. (2017). A tutorial on bridge sampling. arXiv:1703.05984
- Hoijtink, H., Klugkist, I., & Boelen, P. (2008).
*Bayesian evaluation of informative hypotheses*. Springer Science & Business Media.Google Scholar - Jaynes, E. T. (1986). Bayesian methods: General background In In J.H. Justice, & E.T. Jaynes (Eds.),
*Maximum entropy and Bayesian methods in applied statistics*, (pp. 1–25). Cambridge: Cambridge University Press. Retrieved from http://tinyurl.com/jaynes1986 - Jaynes, E.T. (2003).
*Probability theory: The logic of science*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Jeffreys, H. (1936). Xxviii. on some criticisms of the theory of probability.
*The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science*,*22*(146), 337–359. doi: 10.1080/14786443608561691. Retrieved from http://www.tandfonline.com/doi/pdf/10.1080/14786443608561691.CrossRefGoogle Scholar - Jeffreys, H. (1961).
*Theory of probability*, 3rd edn. Oxford, UK: Oxford University Press.Google Scholar - Kaplan, D., & Depaoli, S. (2012). Bayesian structural equation modeling In In R. Hoyle, D. Kaplan, & S. Depaoli (Eds.),
*Handbook of structural equation modeling*, (pp. 650–673). New York, NY: Guilford. Retrieved from http://tinyurl.com/kaplan2012 - Kass, R. E., & Raftery, A. E. (1995). Bayes factors.
*Journal of the American Statistical Association*,*90*, 773–795. Retrieved from http://tinyurl.com/KassRaftery CrossRefGoogle Scholar - Kruschke, J. K. (2015).
*Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan*. Academic Press. Retrieved from http://tinyurl.com/kruschke2015 - Kruschke, J. K., & Liddell, T. (this issue). Bayesian data analysis for newcomers.
*Psychonomic Bulletin and Review*.Google Scholar - Lee, M. D. (2008). Three case studies in the Bayesian analysis of cognitive models.
*Psychonomic Bulletin and Review*,*15*(1), 1–15. Retrieved from http://tinyurl.com/lee2008cognitive CrossRefPubMedGoogle Scholar - Lee, M. D., & Vanpaemel, W. (this issue). Determining priors for cognitive models.
*Psychonomic Bulletin & Review*. Retrieved from https://webfiles.uci.edu/mdlee/LeeVanpaemel2016.pdf - Lee, M. D., & Wagenmakers, E.J. (2014).
*Bayesian cognitive modeling: A practical course*. Cambridge: Cambridge University Press.Google Scholar - Lehmann, E. (1993). The Fisher, Neyman–Pearson theories of testing hypotheses: One theory or two?
*Journal of the American Statistical Association*,*88*(424), 1242–1249.CrossRefGoogle Scholar - Lindley, D.V. (1972).
*Bayesian statistics, a review*. Philadelphia, PA: SIAM.CrossRefGoogle Scholar - Lindley, D. V. (1993). The analysis of experimental data: The appreciation of tea and wine.
*Teaching Statistics*,*15*(1), 22–25. doi: 10.1111/j.1467-9639.1993.tb00252.x.CrossRefGoogle Scholar - Lindley, D. V. (2000). The philosophy of statistics.
*The Statistician*,*49*(3), 293–337. Retrieved from http://tinyurl.com/lindley2000 Google Scholar - Lindley, D.V. (2006).
*Understanding uncertainty*. New York: John Wiley & Sons.CrossRefGoogle Scholar - Love, J., Selker, R., Marsman, M., Jamil, T., Dropmann, D., Verhagen, J., ..., & Wagenmakers, E.-J. (2015). JASP (version 0.7.1.12).
*Computer Software*.Google Scholar - Ly, A., Verhagen, A. J., & Wagenmakers, E.-J. (2016). Harold Jeffreys’s default Bayes factor hypothesis tests: Explanation, extension, and application in psychology.
*Journal of Mathematical Psychology*,*72*, 19–32. Retrieved from http://tinyurl.com/zyvgp9y http://tinyurl.com/zyvgp9y CrossRefGoogle Scholar - Matzke, D., Boehm, U., & Vandekerckhove, J. (this issue). Bayesian inference for psychology, Part III: Parameter estimation in nonstandard models.
*Psychonomic Bulletin and Review*.Google Scholar - Mayer, J., Khairy, K., & Howard, J. (2010). Drawing an elephant with four complex parameters.
*American Journal of Physics*,*78*(6), 648–649. Retrieved from http://tinyurl.com/gtz9w3q CrossRefGoogle Scholar - McElreath, R. (2016).
*Statistical rethinking: A Bayesian course with examples in R and Stan (Vol. 122)*. Boca Raton: CRC Press.Google Scholar - Meng, X.-L., & Wong, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration.
*Statistica Sinica*, 831–860.Google Scholar - Morey, R. D., Romeijn, J.-W., & Rouder, J. N. (2016). The philosophy of Bayes factors and the quantification of statistical evidence.
*Journal of Mathematical Psychology*. Retrieved from http://tinyurl.com/BFphilo - Myung, I. J., & Pitt, M. A. (1997). Applying Occam’s razor in modeling cognition: A Bayesian approach.
*Psychonomic Bulletin & Review*,*4*(1), 79–95. doi: 10.3758/BF03210778. Retrieved from http://tinyurl.com/myung1997.CrossRefGoogle Scholar - Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and continuing controversy.
*Psychological Methods*,*5*(2), 241. doi: 10.1037//1082-989X.S.2.241. Retrieved from http://tinyurl.com/nickerson2000.CrossRefPubMedGoogle Scholar - Open Science Collaboration. (2015). Estimating the reproducibility of psychological science.
*Science*,*349*(6251), aac4716. doi: 10.1126/science.aac4716.CrossRefGoogle Scholar - Orwell, G. (1946). A nice cup of tea.
*Evening Standard, January*.Google Scholar - Robert, C. P. (2014). On the Jeffreys-Lindley paradox.
*Philosophy of Science*,*81*(2), 216–232. Retrieved from http://www.jstor.org/stable/10.1086/675729 CrossRefGoogle Scholar - Rouder, J. N. (2014). Optional stopping: No problem for Bayesians.
*Psychonomic Bulletin & Review*,*21*(2), 301–308. doi: 10.3758/s13423-014-0595-4. Retrieved from http://tinyurl.com/rouder2014.CrossRefGoogle Scholar - Rouder, J. N., Engelhardt, C. R., McCabe, S., & Morey, R. D. (2016). Model comparison in ANOVA.
*Psychonomic Bulletin & Review*,*23*, 1779–1786.CrossRefGoogle Scholar - Rouder, J. N., & Lu, J. (2005). An introduction to Bayesian hierarchical models with an application in the theory of signal detection.
*Psychonomic Bulletin & Review*,*12*(4), 573–604. Retrieved from http://tinyurl.com/rouder2005 CrossRefGoogle Scholar - Rouder, J. N., & Morey, R. D. (2012). Default Bayes factors for model selection in regression.
*Multivariate Behavioral Research*,*47*(6), 877–903. doi: 10.1080/00273171.2012.734737. Retrieved from http://tinyurl.com/rouder2012regression.CrossRefPubMedGoogle Scholar - Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs.
*Journal of Mathematical Psychology*,*56*(5), 356–374. Retrieved from http://tinyurl.com/rouder2012an CrossRefGoogle Scholar - Rouder, J. N., Morey, R. D., Verhagen, J., Province, J. M., & Wagenmakers, E.-J. (2016). Is there a free lunch in inference?
*Topics in Cognitive Science*,*8*, 520–547. Retrieved from http://tinyurl.com/jjubz9y CrossRefPubMedGoogle Scholar - Rouder, J. N., Morey, R. D., Verhagen, J., Swagman, A. R., & Wagenmakers, E.-J (in press). Bayesian analysis of factorial designs.
*Psychological Methods*. Retrieved from http://tinyurl.com/zh4bkt8 - Rouder, J. N., Morey, R. D., & Wagenmakers, E.-J. (2016). The interplay between subjectivity, statistical practice, and psychological science.
*Collabra*,*2*(1). Retrieved from http://www.collabra.org/article/10.1525/collabra.28/ - Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian
*t*-tests for accepting and rejecting the null hypothesis.*Psychonomic Bulletin and Review*,*16*(2), 225–237. doi: 10.3758/PBR.16.2.225. Retrieved from http://tinyurl.com/rouder2009.CrossRefPubMedGoogle Scholar - Rouder, J. N., & Vandekerckhove, J. (this issue). Bayesian inference for psychology, Part IV: Parameter estimation and Bayes factors.
*Psychonomic Bulletin and Review*.Google Scholar - Royall, R. (1997).
*Statistical evidence: A likelihood paradigm (Vol. 77)*. Boca Raton: CRC Press.Google Scholar - Royall, R. (2004). The likelihood paradigm for statistical inference In In M.L. Taper, & S.R. Lele (Eds.),
*The nature of scientific evidence: Statistical, philosophical and empirical considerations*, (pp. 119–152). Chicago: The University of Chicago Press. Retrieved from http://tinyurl.com/royall2004 - Schönbrodt, F. D., & Wagenmakers, E.-J. (this issue). Bayes factor design analysis: Planning for compelling evidence.
*Psychonomic Bulletin and Review*.Google Scholar - Schönbrodt, F. D., Wagenmakers, E.-J., Zehetleitner, M., & Perugini, M. (2015). Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences.
*Psychological Methods*. Retrieved from http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2604513. doi: 10.1037/met0000061 - Senn, S. (2013). Invalid inversion.
*Significance*,*10*(2), 40–42. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1740-9713.2013.00652.x/full CrossRefGoogle Scholar - Sorensen, T., Hohenstein, S., & Vasishth, S. (2016). Bayesian linear mixed models using Stan: A tutorial for psychologists, linguists, and cognitive scientists.
*The Quantitative Methods for Psychology*(3). Retrieved from http://www.tqmp.org/RegularArticles/vol12-3/p175/p175.pdf. doi: 10.20982/tqmp.12.3.p175 - Stone, J. V. (2013).
*Bayes’ rule: A tutorial introduction to Bayesian analysis*. Sebtel Press.Google Scholar - Trafimow, D., & Marks, M. (2015). Editorial.
*Basic and Applied Social Psychology*,*37*(1), 1–2. doi: 10.1080/01973533.2015.1012991 CrossRefGoogle Scholar - Vandekerckhove, J., Matzke, D., & Wagenmakers, E.-J. (2015). Model comparison and the principle of parsimony In In J. Busemeyer, J. Townsend, Z. J. Wang, A. Eidels, J. Vandekerckhove, D. Matzke, & E.-J. Wagenmakers (Eds.),
*Oxford handbook of computational and mathematical psychology*(pp. 300–317). Oxford: Oxford University Press. Retrieved from http://tinyurl.com/vandekerckhove2015 - van de Schoot, R., Kaplan, D., Denissen, J., Asendorpf, J. B., Neyer, F. J., & Aken, M. A (2014). A gentle introduction to Bayesian analysis: Applications to developmental research .
*Child Development*,*85*(3), 842–860. Retrieved from http://tinyurl.com/vandeschoot - Van de Schoot, R., Winder, S., Ryan, O., Zondervan-Zwijnenburg, M., & Depaoli, S. (in press). A systematic review of Bayesian papers in psychology: The last 25 years.
*Psychological Methods*.Google Scholar - Vanpaemel, W. (2010). Prior sensitivity in theory testing: An apologia for the Bayes factor.
*Journal of Mathematical Psychology*,*54*, 491–498. doi: 10.1016/j.jmp.2010.07.003. Retrieved from http://tinyurl.com/vanpaemel2010.CrossRefGoogle Scholar - van Ravenzwaaij, D., Cassey, P., & Brown, S. (this issue). A simple introduction to Markov chain Monte-Carlo sampling.
*Psychonomic Bulletin and Review*.Google Scholar - van Ravenzwaaij, D., Boekel, W., Forstmann, B. U., Ratcliff, R., & Wagenmakers, E.- J. (2014). Action video games do not improve the speed of information processing in simple perceptual tasks.
*Journal of Experimental Psychology: General*,*143*(5), 1794–1805. doi: 10.1037/a0036923. Retrieved from http://tinyurl.com/vanRavenzwaaij. - Verhagen, J., & Wagenmakers, E.-J. (2014). Bayesian tests to quantify the result of a replication attempt.
*Journal of Experimental Psychology: General*,*143*(4), 14–57. doi: 10.1037/a0036731. Retrieved from http://tinyurl.com/verhagen2014.Google Scholar - Wagenmakers, E.-J. (2007). A practical solution to the pervasive problems of
*p*values.*Psychonomic Bulletin and Review*,*14*(5), 779–804. Retrieved from http://tinyurl.com/wagenmakers2007 CrossRefPubMedGoogle Scholar - Wagenmakers, E.-J., Lodewyckx, T., Kuriyal, H., & Grasman, R. (2010). Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method.
*Cognitive Psychology*,*60*(3), 158–189. doi: 10.1016/j.cogpsych.2009.12.001. Retrieved from http://tinyurl.com/wagenmakers2010.CrossRefPubMedGoogle Scholar - Wagenmakers, E.-J., Love, J., Marsman, M., Jamil, T., Ly, A., Verhagen, J., ..., & Morey, R. D. (this issue). Bayesian inference for psychology, Part II: Example applications with JASP.
*Psychonomic Bulletin and Review*.Google Scholar - Wagenmakers, E.-J., Marsman, M., Jamil, T., Ly, A., Verhagen, J., Love, J., ..., & Morey, R. (this issue). Bayesian inference for psychology, Part I: Theoretical advantages and practical ramifications.
*Psychonomic Bulletin and Review*.Google Scholar - Wagenmakers, E.-J., Morey, R. D., & Lee, M. (2016). Bayesian benefits for the pragmatic researcher.
*Current Directions in Psychological Science*,*25*(3). Retrieved from https://osf.io/3tdh9/ - Wagenmakers, E.-J., Verhagen, J., & Ly, A. (2015). How to quantify the evidence for the absence of a correlation.
*Behavior Research Methods*, 1–14.Google Scholar - Wetzels, R., Matzke, D., Lee, M. D., Rouder, J. N., Iverson, G. J., & Wagenmakers, E.- J. (2011). Statistical evidence in experimental psychology: An empirical comparison using 855
*t*-tests.*Perspectives on Psychological Science*,*6*(3), 291–298. doi: 10.1177/1745691611406923. Retrieved from http://tinyurl.com/wetzels2011.CrossRefPubMedGoogle Scholar - Winkler, R. L. (2003).
*An introduction to Bayesian inference and decision*, 2nd edn. Holt, Rinehart and Winston: New York.Google Scholar