Gentle introduction to Bayesian statistics

Bayesian methods are becoming more popular in the social sciences because they offer solutions to problems that arise with classical methods, e.g., convergence issues and the inability to interpret the results probabilistically. However, Bayesian statistics remain controversial because they require specifying prior distributions that reflect the researcher’s state of knowledge before observing the data. Critics of Bayesian statistics note that prior distributions allow researchers to sway the results in the desired direction. This chapter shows how to conduct a Bayesian mediation analysis using real data from a study of delays in PhD completion in the Netherlands. The authors illustrate the challenges in specifying prior distributions and how to examine the influence of a prior distribution in a sensitivity analysis. The chapter also contains detailed examples of how to report the results of a Bayesian mediation analysis and future directions for the field of applied statistics for social sciences.