What is the point of Bayesian analysis?

In her compelling historical account of the development of Bayesian statistical theory, Sharon Bertsch McGrayne recounts how Bayesian thinking has long engendered controversy and negative reactions, particularly within a statistical (and broader scientific) community that for much of the 20th century was dominated by a few key thought leaders fiercely opposed to the approach (i.e., “anti-Bayesians”). Now, in the 21st century, modern computing has made Bayesian analysis more feasible and accessible, and the ways in which Bayesian thinking can advance scientific inquiry, including in medical research, have begun to be realized. During the coronavirus disease (COVID-19) pandemic, the Bayesian approach was used in adaptive clinical trial designs, enabling more timely and efficient evaluation of potential therapies. Some of these trials changed clinical practice, suggesting that the clinical community is ready to embrace Bayesian analysis in clinical trials. Yet, some still view the Bayesian approach with a measure of skepticism because it has led to marked (and sometimes favorable) reinterpretations of data, particularly for randomized trials. That different statistical frameworks, one of which explicitly admits prior information, yield competing interpretations seems to introduce a kind of epistemic fog into our work. Can we establish the truth about an intervention’s effect? And are the seemingly positive results of Bayesian analysis too good to be true?

Ewan C Goligher, Michael O Harhay