Credible Confidence: A Pragmatic View on the Frequentist vs Bayesian Debate

The debate between Bayesians and frequentist statisticians has been going on for decades. Whilst there are fundamental theoretical and philosophical differences between both schools of thought, we argue that in two most common situations the practical differences are negligible when off-the-shelf Bayesian analysis (i.e., using 'objective' priors) is used. We emphasize this reasoning by focusing on interval estimates: confidence intervals and credible intervals. We show that this is the case for the most common empirical situations in the social sciences, the estimation of a proportion of a binomial distribution and the estimation of the mean of a unimodal distribution. Numerical differences between both approaches are small, sometimes even smaller than those between two competing frequentist or two competing Bayesian approaches. We outline the ramifications of this for scientific practice.