I hoped we were past the point where people describe priors as "subjective". Sigh. Bayes formula can be applied with complete objectivity. Inference given the same starting knowledge plus the same evidence will always yield the same conclusion. It need not be subjective, but it IS relative to one's knowledge. And why is that a bad thing? Shouldn't more knowledge == better inference? We have a systematic way to build knowledge with reasonable objectivity (the scientific method) - should we not use it? Or do these people literally believe that less knowledge somehow improves their decision making?
It seems that there’s still unavoidable subjectivity in making the choice of prior distribution? I get how it’s objective for a fixed choice, but my understanding is that you need to first make that choice in order to be objective. Is it actually that making your choice of prior is obvious (or there is some objectively optimal way to pick a prior), which rules out any subjectivity in the choice of prior?
There is also unavoidable subjectivity in making the choice of model, data, etc.
Yes. You've hit the essence of the problem - the choice of a prior. The scientific method gives us a way to choose a prior that fits reality. You are claiming something different, that our prior is based on subjective choices. Yep, those are both ways to choose a prior. But only one is guaranteed to be valid. Do I even need to mention the appalling history of base rate neglect in medical research? Neglecting priors leads to bad decisions.
Re:The Bayesian Cringe (2021)
by silent_cal on Wednesday March 27, 2024 @10:38AM
(#39839780)
And yet nobody asks "how did you come up with that .05 significance level?"
Yet when I lay out fairly tight Bayesian reasoning, there's always that one person sucking life out of the entire conversation with "Wait can you go back to that first number? How did you arrive at that?" and it's an unanswerable question because any attempt would have to start from another, more fundamental prior!
Sometimes this person is reasonable and I can go, "Ah, we can try a different starting point. What's your prior?" but often enough the person gets stuck on the idea of subjective probability and everything derails.
When it comes to important decisions, I've started hiding the prior with smoke and mirrors to redirect attention away from it.