> The main reason scientists have historically been resistant to using Bayesian inference instead is that they are afraid of being accused of subjectivity. The prior probabilities required for Bayes’ rule feel like an unseemly breach of scientific ethics. Where do these priors come from?
It's not just "being afraid"; the problem is that random guessing (of priors) is not a reasonable replacement for science.
Bayes' rule is great if you can find a reasonable justification for a prior. Bayes is widely used for decision-making (for example), where you need an answer quickly & you aren't trying to make general scientific claims. But if you can't find a justifiable prior in a scientific work, using Bayes' rule just replaces one statistical fallacy for another one. After all, Bayes' rule will give nonsense answers if you give it a nonsense prior!
Bayes' rule is a great tool in many circumstances! But it has a great weakness: it requires a prior. That doesn't make it useless; few tools are useful in all circumstances. But requiring "everyone to use Bayes' rule, even though we have no reasonable way to find a good estimate of the priors," is unlikely to ever happen (and rightly so). The article rightly points out a serious problem with the typical application of statistics, but there needs to be a better justification for priors than is suggested in this article.
I could imagine systemic worldwide ways to deal with this. For example, perhaps the scientific community could allow people to propose initial priors, and then allow multiple different papers to improve the estimation of the probability over time. But that would require much more than articles repeatedly saying "there's no serious problem with priors"; having a justifiable way to estimate and update priors is the fundamental problem with Bayesian analysis in the scientific community.