I broadly agree with you, but I'm wondering if you would reconsider your qualification as "less complicated" if you consider beginner learners. E.g. someone who knows basic descriptive statistics and probability theory, and is making first contact with inferential statistics. Specifically, assume a learner who knows what an integral is, but is far from proficient with it (UGRAD student, not a GRAD student).
I was reading this paper[1] recently, which highlights two difficulties of teaching Bayesian stats: 1) the mathematical complexity of understanding conditional probability distributions, and 2) the lack of well defined, broadly accepted conventions for what priors to use in specific data analysis scenarios.
I think a computational approach to prob theory could mitigate 1), but 2) remains a problem—the freedom to choose priors, is also a burden...
[1] https://www.stat.purdue.edu/~dsmoore/articles/BayesPedagogy....
Maybe someone here might have suggestions?
The closest thing that comes to mind is "Bayes factors," which has some traction (usage), but apparently they have lots of problems and limitations too, cf. https://www.youtube.com/watch?v=MqeWpR6S4XA
The canonical approach is to build a generative model with a parameter (or multiple for ~anova) that codes for the difference between groups and do inference on that parameter of interest. Most of the recipes taught in statistics classes can be modelled as a regression of some kind (this counts for frequentist stats too, see https://lindeloev.github.io/tests-as-linear/ ). Some advocate to do that inference with bayes factors. Others, like discussed elsewhere in this thread, advocate combining the resulting posterior with a cost/value function, but either way the lesson is that there is less focus on "t-test-vs-anova" because they're the same thing anyways.
I had previously started the BDA course, which is another famous Bayesian course, see https://avehtari.github.io/BDA_course_Aalto/ but I didn't finish it due to travel.
No more excuses in 2024... time to level-up the Bayesian modelling skill ;)
Of course the winners don't rant about anything. But any time we probe the consequences of Frequentist statistics they turn out to be horrific for science, our health, and our planet.
Bayesian statistics is sound but I suspect it's often just used to justify biases. It is technically valid to use a prior and de facto never update it, because you know I'll get around to updating my prior next week, or... eventually, cough cough let's be honest, never
It's the frequentist one that gets your biases implicitly, on the form of corrections and hypothesis formulation, so that people don't notice them.
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.