3 ms·
I don't know. I've published Bayesian methodology papers and reviewed them and although I might call myself an objective Bayesianist maybe, Bayesianism has its
by derbOac 3y ago
I don't know. I've published Bayesian methodology papers and reviewed them and although I might call myself an objective Bayesianist maybe, Bayesianism has its own implicit biases. In the very least, I think it can take advantage of implicit biases people have in interpreting analyses.
One issue is that Bayes estimates are almost always produced, even if no information is coming from empirical data, and all the information is coming from a prior. So it's possible to produce results heavily influenced by the prior with Bayesian estimation that with frequentist methods would fail completely because of lack of identification of the model, sending a strong signal that something is wrong. This can all be sussed out with Bayesian methods but people often don't do it.
Another more subtle issue is people aren't quite aware of how a prior can deviate from "maximal conservativism". Sometimes, for example, depending on the model, a very flat prior is actually not conservative, and is overweighting tails.
There's other examples too. Basically, yes, Bayesianism forces you to be explicit with your biases, but people are really bad at interpreting the actual impact of those biases in a formal Bayesian framework, or at least, aren't any better at it than with frequentist methods that are available.
If you approach statistical inference from the perspective of accuracy (as the linked paper seems to do) Bayesianism is better to the extent the priors are accurate. This is true a lot of the time empirically, but it does lead to a kind of tautology, in that you're doing the analysis because you don't really know what "truth" is. So if you're right in your priors, Bayesianism is accurate, but then you didn't really need new data as much in the first place; if you're wrong, it's more biased. Basically in the bias-variance tradeoff, Bayesianism makes a bet on reduced variance assuming that the resulting bias will be small enough.
Philosophically, though, there's a completely different argument, which is one of competitive fairness. You might say this doesn't matter, but consider consequential decisions, like hiring or admissions decisions: if someone was making a prediction about you, would you want them to use a strong prior, or something that's maximally conservative and fair?
This philosophy leads to frequentism basically.
My preference is to be maximally conservative in a Bayesian framework, which leads to reference priors, which are often flat in many canonical situations, which is basically frequentism. In other situations you might have a different kind of prior.
To me the linked paper is pretty interesting and makes a good point. On the other hand, I'd rather not make any assumptions about a new result based on past studies on other effects. I'd rather just collect lots of diverse real data and meta-analyze it. There's no substitute for data -- and that includes priors.