Identical twins and Bayes' theorem in the 21st century

Abstract

In a recent article in Science on "Bayes' Theorem in the 21st Century", Bradley Efron uses Bayes' theorem to calculate the probability that twins are identical given that the sonogram shows twin boys. He concludes that Bayesian calculations cannot be uncritically accepted when using uninformative priors. We argue that this conclusion is problematic because Efron's example on identical twins does not use data, hence it is not Bayesian statistics; his priors are not appropriate and are not uninformative; and using the available data point and an uninformative prior actually leads to a reasonable posterior distribution.