# References

Bürkner, Paul-Christian. 2017. “brms: An R Package for Bayesian Multilevel Models Using Stan.” Journal of Statistical Software 80 (1): 1–28. https://doi.org/10.18637/jss.v080.i01.

Carvalho, Carlos M, Nicholas G Polson, and James G Scott. 2009. “Handling Sparsity via the Horseshoe.” In Artificial Intelligence and Statistics, 73–80.

Frank, Avi, Sena Biberci, and Bruno Verschuere. 2019. “The language of lies: a preregistered direct replication of Suchotzki and Gamer (2018; Experiment 2).” Cognition and Emotion 33 (6): 1310–5. https://doi.org/10.1080/02699931.2018.1553148.

Gelman, Andrew. 2006. “Prior distributions for variance parameters in hierarchical models (Comment on Article by Browne and Draper).” Bayesian Analysis 1 (3): 515–34. https://doi.org/10.1214/06-BA117A.

Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald Rubin. 2013. Bayesian Data Analysis. 3rd ed. London, UK: CRC Press.

Gelman, Andrew, Jennifer Hill, and Masanao Yajima. 2012. “Why we (usually) don’t have to worry about multiple comparisons.” Journal of Research on Educational Effectiveness 5 (2): 189–211. https://doi.org/10.1080/19345747.2011.618213.

Gelman, Andrew, Aleks Jakulin, Maria Grazia Pittau, and Yu-Sung Su. 2008. “A Weakly Informative Default Prior Distribution for Logistic and Other Regression Models.” The Annals of Applied Statistics, 1360–83.

Gelman, Andrew, Xiao-Li Meng, and Hal Stern. 1996. “Posterior Predictive Assessment of Model Fitness via Realized Discrepancies.” Statistica Sinica, 733–60.

Gigerenzer, Gerd. 2004. “Mindless statistics.” The Journal of Socio-Economics 33 (5): 587–606. https://doi.org/10.1016/j.socec.2004.09.033.

Heathcote, Andrew, Scott Brown, and Denis Cousineau. 2004. “QMPE: Estimating Lognormal, Wald, and Weibull Rt Distributions with a Parameter-Dependent Lower Bound.” Behavior Research Methods, Instruments, & Computers 36 (2): 277–90.

Hedeker, Donald, Robin J. Mermelstein, and Hakan Demirtas. 2008. “An application of a mixed-effects location scale model for analysis of ecological momentary assessment (EMA) data.” Biometrics 64 (2): 627–34. https://doi.org/10.1111/j.1541-0420.2007.00924.x.

Hoeting, Jennifer A, David Madigan, Adrian E Raftery, and Chris T Volinsky. 1999. “Bayesian Model Averaging: A Tutorial.” Statistical Science, 382–401.

Kruschke, John K. 2013. “Bayesian estimation supersedes the t test.” Journal of Experimental Psychology: General 142 (2): 573–603. https://doi.org/10.1037/a0029146.

———. 2015. Doing Bayesian Data Analysis: Tutorial with R, JAGS, and Stan. 2nd ed. London, UK: Academic Press.

Kruschke, John K, and Torrin M Liddell. 2018. “The Bayesian new statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.” Psychonomic Bulletin & Review 25 (1): 178–206. https://doi.org/10.3758/s13423-016-1221-4.

Lai, Mark H. C., and Oi-man Kwok. 2015. “Examining the Rule of Thumb of Not Using Multilevel Modeling: The ‘Design Effect Smaller Than Two’ Rule.” The Journal of Experimental Education 83: 423–38. https://doi.org/10.1080/00220973.2014.907229.

Lambert, Ben. 2018. A student’s guide to Bayesian statistics. https://bookshelf.vitalsource.com.

McElreath, Richard. 2016. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Vol. 122. CRC Press.

Piironen, Juho, and Aki Vehtari. 2016. “Comparison of Bayesian Predictive Methods for Model Selection.” Statistics and Computing.

Pritschet, Laura, Derek Powell, and Zachary Horne. 2016. “Marginally Significant Effects as Evidence for Hypotheses: Changing Attitudes over Four Decades.” Psychological Science 27 (7): 1036–42.

Silberzahn, Raphael, Eric L Uhlmann, Daniel P Martin, Pasquale Anselmi, Frederik Aust, Eli Awtrey, Štěpán Bahnı́k, et al. 2018. “Many Analysts, One Data Set: Making Transparent How Variations in Analytic Choices Affect Results.” Advances in Methods and Practices in Psychological Science 1 (3): 337–56.

Thoemmes, Felix, and Norman Rose. 2014. “A Cautious Note on Auxiliary Variables That Can Increase Bias in Missing Data Problems.” Multivariate Behavioral Research 49 (5): 443–59.

Van Buuren, Stef. 2018. Flexible Imputation of Missing Data. 2nd ed. Boca Raton, FL: CRC Press. https://stefvanbuuren.name/fimd/.

van de Schoot, Rens, Sonja D. Winter, Oisín Ryan, Mariëlle Zondervan-Zwijnenburg, and Sarah Depaoli. 2017. “A systematic review of Bayesian articles in psychology: The last 25 years.” Psychological Methods 22 (2): 217–39. https://doi.org/10.1037/met0000100.

Vehtari, Aki, Andrew Gelman, and Jonah Gabry. 2016. “Practical Bayesian Model Evaluation Using Leave-One-Out Cross-Validation and Waic.” Statistics and Computing 27 (5): 1413–32. https://doi.org/10.1007/s11222-016-9696-4.

Yao, Yuling, Aki Vehtari, Daniel Simpson, and Andrew Gelman. 2018. “Using stacking to average bayesian predictive distributions (with discussion).” Bayesian Analysis 13 (3): 917–1007. https://doi.org/10.1214/17-BA1091.

1. Price is another important figure in mathematics and philosopher, and have taken Bayes’ theorem and applied it to insurance and moral philosophy.↩︎

2. See the paper by John Aldrich on this.↩︎

4. In a purely subjectivist view of probability, assigning a probability $$P$$ to an event does not require any justifications, as long as it follows the axioms of probability. For example, I can say that the probability of me winning the lottery and thus becoming the richest person on earth tomorrow is 95%, which by definition would make the probability of me not winning the lottery 5%. Most Bayesian scholars, however, do not endorse this version of subjectivist probability, and require justifications of one’s beliefs (that has some correspondence to the world).↩︎
5. The likelihood function in classical/frequentist statistics is usually written as $$P(y; \theta)$$. You will notice that here I write the likelihood for classical/frequentist statistics to be different than the one used in Bayesian statistics. This is intentional: In frequentist conceptualization, $$\theta$$ is fixed and it does not make sense to talk about probability of $$\theta$$. This implies that we cannot condition on $$\theta$$, because conditional probability is defined only when $$P(\theta)$$ is defined.↩︎