[RandomThoughts3]

I’m always puzzled by this because while I come from a country where the frequentist approach generally dominates, the fight with Bayesian basically doesn’t exist. That’s just a bunch of mathematical theories and tools. Just use what’s useful.

I’m still convinced that Americans tend to dislike the frequentist view because it requires a stronger background in mathematics.

[parpfish]

I don’t think mathematical ability has much to do with it.

I think it’s useful to break down the anti-Bayesians into statisticians and non-statistician scientists.

The former are mathematically savvy enough to understand bayes but object on philosophical grounds; the later don’t care about the philosophy so much as they feel like an attack on frequentism is an attack on their previous research and they take it personally

[mturmon]

This is a reasonable heuristic. I studied in a program that (for both philosophical and practical reasons) questioned whether the Bayesian formalism should be applied as widely as it is. (Which for many people is, basically everywhere.)

There are some cases, that do arise in practice, where you can’t impose a prior, and/or where the “Dutch book” arguments to justify Bayesian decisions don’t apply.

[runarberg]

I think the distaste Americans have to frequentists has much more to do with history of science. The Eugenics movement had a massive influence on science in America a and they used frequentist methods to justify (or rather validate) their scientific racism. Authors like Gould brought this up in the 1980s, particularly in relation to factor analysis and intelligence testing, and was kind of proven right when Hernstein and Murray published The Bell Curve in 1994.

The p-hacking exposures of the 1990s only fermented the notion that it is very easy to get away with junk science using frequentest methods to unjustly validate your claims.

That said, frequentists are still the default statistics in social sciences, which ironically is where the damage was the worst.

[TeaBrain]

I don't think the guy's basic assertion is true that frequentist statistics is less favored in American academia.

[runarberg]

I’m not actually in any statistician circles (although I did work at a statistical startup that used Kalman Filters in Reykjavík 10 years ago; and I did dropout from learning statistics in University of Iceland).

But what I gathered after moving to Seattle is that Bayesian statistics are a lot more trendy (accepted even) here west of the ocean. Frequentists is very much the default, especially in hypothesis testing, so you are not wrong. However I’m seeing a lot more Bayesian advocacy over here than I did back in Iceland. So I’m not sure my parent is wrong either, that Americans tend to dislike frequentist methods, at least more than Europeans do.

[lupire]

What is the protection against someone using a Bayesian analysis but abusing it with hidden bias?

[runarberg]

I’m sure there are creative ways to misuse bayesian statistics, although I think it is harder to hide your intentions as you do that. With frequentist approaches your intentions become obscure in the whole mess of computations and at the end of it you get to claim this is a simple “objective” truth because the p value shows < 0.05. In bayesan statistics the data you put into it is front and center: The chances of my theory being true given this data is greater than 95% (or was it chances of getting this data given my theory?). In reality most hoaxes and junk science was because of bad data which didn’t get scrutinized until much too late (this is what Gould did).

But I think the crux of the matter is that bad science has been demonstrated with frequentists and is now a part of our history. So people must either find a way to fix the frequentist approaches or throw it out for something different. Bayesian statistics is that something different.

[lottin]

> "The chances of my theory being true given this data is greater than 95% (or was it chances of getting this data given my theory?)"

The first statement assumes that parameters (i.e. a state of nature) are random variables. That's the Bayesan approach. The second statement assumes that parameters are fixed values, not random, but unknown. That's the frequentist approach.

[analog31]

My knee jerk reaction is replication, and studying a problem from multiple angles such as experimentation and theory.

[ordu]

I'd suggest you to read "The Book of Why"[1]. It is mostly about Judea's Pearl next creation, about causality, but he also covers bayesian approach, the history of statistics, his motivation behind bayesian statistics, and some success stories also.

To read this book will be much better, then to apply "Hanlon's Razor"[2] because you see no other explanation.

[1] https://en.wikipedia.org/wiki/The_Book_of_Why

[2] https://en.wikipedia.org/wiki/Hanlon's_razor

[gnulinux]

This statement is correct only on a very basic, fundamental sense, but it disregards the research practice. Let's say you're a mathematician who studies analysis or algebra. Sure, technically there is no fundamental reason for constructive logic and classical logic to "compete", you can simply choose whichever one is useful for the problem you're solving, in fact {constructive + lem + choice axioms} will be equivalent to classical math, so why not just study constructive math since it's higher level of abstraction and you can always add those axioms "later" when you have a particular application.

In reality, on a human level, it doesn't work like that because, when you have disagreements on the very foundations of your field, although both camps can agree that their results do follow, the fact that their results (and thus terminology) are incompatible makes it too difficult to research both at the same time. This basically means, practically speaking, you need to be familiar with both, but definitely specialize in one. Which creates hubs of different sorts of math/stats/cs departments etc.

If you're, for example, working on constructive analysis, you'll have to spend tremendous amount of energy on understanding contemporary techniques like localization etc just to work around a basic logical axiom, which is likely irrelevant to a lot of applications. Really, this is like trying to understand the mathematical properties of binary arithmetic (Z/2Z) but day-to-day studying group theory in general. Well, sure Z/2Z is a group, but really you're simply interested in a single, tiny, finite abelian group, but now you need to do a whole bunch of work on non-abelian groups, infinite groups, non-cyclic groups etc just to ignore all those facts.

[RandomThoughts3]

I would follow but neither Bayesian nor frequentist probabilities are rocket science.

I’m not following your exemple about binary and group theory either. Nobody looks at the properties of binary and stops there. If you are interested in number theory, group theory will be a useful part of your toolbox for sure.

[thegginthesky]

It's because practicioners of one says that the other camp is wrong and question each other's methodologies. And in academia, questioning one's methodology is akin to saying one is dumb.

To understand both camps I summarize like this.

Frequentist statistics has very sound theory but is misapplied by using many heuristics, rule of thumbs and prepared tables. It's very easy to use any method and hack the p-value away to get statistically significant results.

Bayesian statistics has an interesting premise and inference methods, but until recently with the advancements of computing power, it was near impossible to do simulations to validate the complex distributions used, the goodness of fit and so on. And even in the current year, some bayesian statisticians don't question the priors and iterate on their research.

I recommend using methods both whenever it's convenient and fits the problem at hand.

[bb86754]

I can attest that the frequentist view is still very much the mainstream here too and fills almost every college curriculum across the United States. You may get one or two Bayesian classes if you're a stats major, but generally it's hypothesis testing, point estimates, etc.

Regardless, the idea that frequentist stats requires a stronger background in mathematics is just flat out silly though, not even sure what you mean by that.

[blt]

I also thought it was silly, but maybe they mean that frequentist methods still have analytical solutions in some settings where Bayesian methods must resort to Monte Carlo methods?

[kgwgk]

Note that Bayesian methods also have analytical solutions in some settings.

There is a reason why conjugate priors were a thing.

[ants_everywhere]

> I’m still convinced that Americans tend to dislike the frequentist view because it requires a stronger background in mathematics.

The opposite is true. Bayesian approaches require more mathematics. The Bayesian approach is perhaps more similar to PDE where problems are so difficult that the only way we can currently solve them is with numerical methods.