Comment on "Bayes' Theorem in the 21st Century" by Bradley Efron

TL;DR

This paper critiques Efron's conclusion on Bayesian methods, arguing that his example is flawed due to misuse of data and priors, and that proper Bayesian analysis with data and uninformative priors is reasonable.

Contribution

It clarifies misconceptions about Bayesian calculations with uninformative priors and emphasizes correct application with data.

Findings

Efron's example does not involve data, thus not truly Bayesian.

His priors are not uninformative and are poorly chosen.

Using data with an uninformative prior yields reasonable posteriors.

Abstract

In a Perspectives article in Science, Bradley Efron concludes that Bayesian calculations cannot be uncritically accepted when using uninformative priors. We argue that this conclusion is problematic because Efron's example does not use data, hence it is not Bayesian statistics; his priors make little sense and are not uninformative; and using the available data point and an uninformative prior actually leads to a reasonable posterior distribution.