> But when one fine day you decide to do something more complex, these are the land mines that you shouldn't really ignore.

> in many real scenarios flat priors are not ok.

> eventually one day you will change lanes on the highway at the exact wrong time, and you will really regret your habit of not looking in your mirror.

Can you give some examples where frequentists hit these alleged flat-prior landmines? I am admittedly a Bayesian by training, not a frequentist, so perhaps it's just my ignorance showing, but I'm not aware of any such situations.

Frequentist statistics generally relies on performance guarantees (bounds on the false positive error rate for tests, in particular, and coverage for confidence intervals) which are derived under the lack-of-explicit-prior, so as far as I can tell they should be doing fine. I'd be interested in seeing examples where frequentist analyses fail because of the (implicit) flat prior.

> we're almost always choosing a very simplistic distribution (e.g. Gaussian) to do this

The Gaussian distribution is a marvelous thing. The central limit theorem is, in my humble opinion, one of the most beautiful and surprising results in mathematics.

> Is it not much better to discuss the full posterior, "degrees of belief" and to be explicit about all of our uncomfortable prior assumptions?

Perhaps I'm just cynical, but I'd say probably not. A Bayesian decision process is still a decision process and still subject to all the problems that the frequentist decision process (null hypothesis significance testing) is subject to: inflated family-wise error rates, p-hacking (except with Bayes factors rather than p-values), publication bias, and so on. At best getting everyone to do Bayesian analyses might be roughly equivalent to getting everyone to use a lower default significance threshold, like 0.005 instead of 0.05 (which prominent statisticians have advocated for).

> I prefer Bayesian model selection over null hypothesis rejection 100% of the time, especially because "Bayesian model selection" is the only logical way to do model selection, the only caveat is that it depends on reasonable prior assumptions and these are the hard part (but again, at least it is explicit!).

Sadly there's a trap in Bayesian model selection (often called Bartlett's paradox, though it's essentially the same thing as Lindley's paradox) which can be difficult to spot. No names out of respect to the victim, but several years ago I saw a very experienced Bayesian statistician who has published papers about Lindley's paradox fall prey to this. Explicit priors didn't help him at all. He would not have fallen into it if he had used a frequentist model selection method, though there are other problems with that.

> Also, the Lindley's "paradox" example certainly seems contrived:

And here we are again calling a statistical test that thousands of people do every day "contrived." You already know how I feel about that.

Yes, it's a very simple example, because that helps illustrate what's happening. Lindley's paradox can happen in arbitrarily complex models, any time you're doing model selection.

> By contrived, I mean that it appears designed to exploit the fact that Bayesian stats will automatically prefer simpler models, especially one with 0 degrees of freedom that is relatively close to the right answer, but that's a Good Thing (TM).

Preferring simpler models is not exactly what's going on in Lindley's paradox, at least not the way that most people talk about Bayes factors preferring simpler models (e.g. by reference to the k*ln(n) term in the Bayesian Information Criterion). The BIC is based on an asymptotic equivalence and drops a constant term. That constant term is actually what is primarily responsible for Lindley's paradox, and has only an indirect relationship to the complexity of the model.