Bayesian inference for psychology, part IV: parameter estimation and Bayes factors
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In the psychological literature, there are two seemingly different approaches to inference: that from estimation of posterior intervals and that from Bayes factors. We provide an overview of each method and show that a salient difference is the choice of models. The two approaches as commonly practiced can be unified with a certain model specification, now popular in the statistics literature, called spike-and-slab priors. A spike-and-slab prior is a mixture of a null model, the spike, with an effect model, the slab. The estimate of the effect size here is a function of the Bayes factor, showing that estimation and model comparison can be unified. The salient difference is that common Bayes factor approaches provide for privileged consideration of theoretically useful parameter values, such as the value corresponding to the null hypothesis, while estimation approaches do not. Both approaches, either privileging the null or not, are useful depending on the goals of the analyst.
KeywordsBayesian inference and parameter estimation Bayesian statistics Model selection
- Berger, J. O., & Wolpert, R. L. (1988). The likelihood principle 2nd Edn. Hayward: Institute of Mathematical Statistics.Google Scholar
- de Finetti, B. (1974) Theory of probability Vol. 1. New York: Wiley.Google Scholar
- Dienes, Z. (2014). Using Bayes to get the most out of non-significant results. Frontiers in Quantitative Psychology and Assessment. Retrieved from https://doi.org/10.3389/fpsyg.2014.00781
- Etz, A., & Vandekerckhove, J. (in press). Introduction to Bayesian inference for psychology. Psychonomic Bulletin & Review. Retrieved from https://osf.io/preprints/psyarxiv/q46q3.
- Gelman, A., & Carlin, J. (2017). Some natural solutions to the p value communication problem—and why they won’t work.Google Scholar
- Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis 2nd Edn. London: Chapman and Hall.Google Scholar
- Jeffreys, H. (1938) Theory of probability. Oxford: Claredon.Google Scholar
- Jeffreys, H. (1961). Theory of probability 3rd Edn. New York: Oxford University Press.Google Scholar
- Kruschke, J. K. (2012). Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General.Google Scholar
- Kruschke, J. K. (2014). Doing Bayesian data analysis 2nd Edn. A tutorial with R, JAGS, and Stan. Waltham MA.: Academic Press.Google Scholar
- Kruschke, J. K., & Liddell, T. M. (2017). The Bayesian new statistics: hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review. Retrieved from http://link.springer.com/article/10.3758/s13423-016-1221-4
- Kruschke, J. K., & Liddell, T. M. (this issue). Bayesian data analysis for newcomers. Psychonomic Bulletin & Review. Retrieved from https://doi.org/10.3758/s13423-017-1272-1
- Lehmann, E. L., & Casella, G. (1998). Theory of point estimation 2nd Edn. New York: Springer.Google Scholar
- Matzke, D., Boehm, U., & Vandekerckhove, J. (this issue). Bayesian inference for psychology, part III: Parameter estimation in nonstandard models. Psychonomic Bulletin & Review.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://www.sciencedirect.com/science/article/pii/S0022249615000723
- Rouder, J. N. (2016). Roll your own: How to compute Bayes factors for your priors. Retrieved from https://osf.io/preprints/psyarxiv/nvsm5 (Archived blog posts).
- Ročková, V., & George, E. L. (2014). EMVS: the EM approach to Bayesian variable selection. Journal of the American Statistical Association, 109.Google Scholar
- Savage, L. J. (1972). The foundations of statistics 2nd Edn. New York: Dover.Google Scholar
- Senn, S. (2011). You may believe you are a Bayesian but you are probably wrong. Rationality, Markets and Morals, 2, 48–66.Google Scholar