> usually experts just eyeball the frequentist results and take a judgment call
Indeed, but that does not make it right or rational. Bayesian method helps keep things rational. This is pertinent because human brains are terrible at conditional probabilities.
One can always argue that data analysis is usually just window dressing and decision making is mostly political and social. Empirically you would be mostly right if you take that position. One cannot argue against that factual observation.
The more interesting question is, if the decision makers aspire to be rational, which method should they use. I have used frequentist and Bayesian methods both. I made the choice on the basis of the question that needed answering.
For example, when we needed to monitor (and alert on) a time varying probability of error (under time varying sample sizes) -- Bayesian method was a more natural fit than say confidence intervals or hypothesis tests. Bayesian methods directly address the question "What is the probability that error probability is below the threshold now, considering domain expert's opinion about how often it goes below the threshold and how the data has looked in the recent past?"
> Indeed, but that does not make it right or rational. Bayesian method helps keep things rational. This is pertinent because human brains are terrible at conditional probabilities.
I agree with you on Bayesian methods keeping things rational (consistent within a probabilistic framework).
I would say there are different kinds of rationality however: the 2 that I'm most interested in are epistemic rationality (not being wrong) and instrumental rationality (what works), and in the domain of business (but perhaps not other domains like science and math), we optimize for the latter. This is because not getting analyses wrong (epistemic) is actually less useful than getting workable results (instrumental) even if the analyses are wrong. In fact, some folks at lesswrong tried their hand at doing a startup, applying all the principles of epistemic rationality and avoiding bias, and it did not work out. Business is less about having the right mental model but doing what works. This article expands on this point [1]
The issue is in ill-defined (not just stochastic in a parametric uncertainty sense, but actually ill-defined) domains like business, the map (statistical models) is not the territory (real world) -- it's a very rough proxy for it. Even the expert opinions that Bayesian methods embed as priors -- many of those are subjective priors which are not 100% rational. Not to be cliched but to recycle an old John Tukey saying: "An approximate answer to the right question is worth a great deal more than a precise answer to the wrong question." Frequentist methods are often good enough for discovering the terrain approximately, and in business, there's more value in discovering terrain than in getting the analysis exactly right.
(that said, in these settings Bayesian methods are equally as good too, though their marginal value over frequentist is often not appreciable. One exception might be multilevel regression analysis where you're stacking models.)
> Even the expert opinions that Bayesian methods embed as priors -- many of those are subjective priors which are not 100% rational.
Of course ! Like big bang it needs one initial allowable 'miracle' and does not let irrationality creep in through other back doors.
As I mentioned earlier, I choose the formulation that suits the question that needs answering.
Not sure about the 'what works' vs 'analytic correctness'. How would even one know that something works or have a hunch about what may succeed if they have no mental model to base it upon. Often that is implicit and not sharp enough to be quantitative. Bayesian formulation helps in making some of those implicit assumptions explicit.
Other than that I think we mostly agree. For example both the formulations have a notion of a completely defined sample space, the universe of all possible outcomes. That works in a game of gambling. In business often you do not know this set.
Anyhow, nice talking to you. I enjoyed the conversation.
Indeed, but that does not make it right or rational. Bayesian method helps keep things rational. This is pertinent because human brains are terrible at conditional probabilities.
One can always argue that data analysis is usually just window dressing and decision making is mostly political and social. Empirically you would be mostly right if you take that position. One cannot argue against that factual observation.
The more interesting question is, if the decision makers aspire to be rational, which method should they use. I have used frequentist and Bayesian methods both. I made the choice on the basis of the question that needed answering.
For example, when we needed to monitor (and alert on) a time varying probability of error (under time varying sample sizes) -- Bayesian method was a more natural fit than say confidence intervals or hypothesis tests. Bayesian methods directly address the question "What is the probability that error probability is below the threshold now, considering domain expert's opinion about how often it goes below the threshold and how the data has looked in the recent past?"