 Finally, one might be interested in how frequently the paradox arises. Simulations by Pavlides and Perlman (2009) suggest that it should not occur frequently: the confidence interval for the probability of AR is a subset of the interval \([0;0.03]\) for both the uniform prior and the (objective) Jeffreys prior. Of course, the practical value of this diagnosis depends on whether the sampling assumptions are sensible, and whether the entire approach makes sense for real-life datasets where researchers can group the data into subpopulations along numerous dimensions.