Browsing through the research area of the top 100 US News statistics program, almost all of them are heavy in Bayesian statistics. However, if I go to lower tier school, most of them are still doing classical/frequentist statistics research. For example, my current school (ranked between 150 to 200 on QS world ranking for stats so not considered a top tier school) has only one professor focusing on Bayesian stats and there is almost a resentment towards Bayesian stats. Some grad students I talked to even says that Bayesian Statisticians are doing Bayesian stats for the sake of it which I of course disagree strongly.

However, I wonder why this is the case. I'm having several educated guesses:

(a) there is not enough room left for advancements in the methodology of classical/frequenting stats and the only viable research in classical/frequentist stats research is on applications which will be the main focus of lower tier school as top tier school should be more inclined towards theoretical and methodological research.

(b) It is heavily field dependent. Certain branch of stats is simply more suitable for Bayesian stats such as many scientific application of stats method while other branch is more suitable for classical stats such as financial area. (correct me if I'm wrong) Given this, it seems to me that top tier schools have a lot of stats faculties doing applications in scientific field while lower tier schools stats department are mainly focusing applications in financial area since that helps them generate income and funding.

(c) There are huge problems with frequentist method that can't be resolved for example the prone to overfitting of MLE, etc. And Bayesian seems to provide a brilliant solutions.

(d) Computational power is here hence Bayesian computation is no longer a bottleneck as it was 30 years ago.

(e) This one may be the most opinionated guess I have. There is a resistance from classical/frequentist Statistician that just don't like a new wave of methodology that can potentially overtake the role of classical stats. But like Larry Wasserman said, it depends on what we are trying to do and everyone should keep an open mind, especially as a researcher.

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    $\begingroup$ While opinions of CV denizens will vary, and such opinionation is considered off-topic, it is worth pointing out that exactly this question is answered in introductory chapters of modern texts on Bayesian analysis. In particular, Chapter 1 of Gelman, et al Bayesian Data Analysis 3rd Ed. It boils down to a) "common sense" and b) the highly problematic frequentist confidence interval that 99% of us can't help but misinterpret. The way we misinterpret it is intrinsically Bayesian, so we might as well do Bayesian analysis from the get-go. $\endgroup$ – Peter Leopold Mar 18 '19 at 14:48
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    $\begingroup$ @Peter Leopold Half seriously: 99%? and who is "us"? Many naive users of statistics indeed have serious misconceptions about CIs, but if you're addressing the CV community, I would hope that 99% really doesn't fit. Statistical people can be just as bad as anyone else at making up numbers in the absence of hard data! $\endgroup$ – Nick Cox Mar 18 '19 at 16:16
  • $\begingroup$ @NickCox I was addressing the OP, and the "us" is meant to be empathetic and inclusive. Hopefully, "99%" is recognized as an order of magnitude estimate $\sim 10^{-2}$. It is also the larger fraction of the have/have-not trope in popular culture, where have-nots in this context indicate the event: "I took stats 101, but I have not fully internalized the frequentist vs. Bayesian interpretation of confidence intervals vs. credible intervals." And now that you called me out, I'll assert (:D) that it is my official prior for that event! Naturally, I am willing to be convinced otherwise! :D $\endgroup$ – Peter Leopold Mar 18 '19 at 17:22

Personally, I would venture a few guesses:

(1) Bayesian statistics saw a huge uptick in popularity in the last couple decades. Part of this was due to advancements in MCMC and improvements in computational resources. Bayesian statistics went from being theoretically really nice but only applicable to toy problems to an approach that could be more universally applied. This means that several years ago, saying you worked on Bayesian statistics probably did make you a very competitive hire.

Now, I would say that Bayesian statistics is still a plus, but so is working on interesting problems without using Bayesian methods. A lack of background in Bayesian statistics would certainly be a minus to most hiring committees, but getting a PhD in statistics without sufficient training in Bayesian methods would be pretty surprising.

(2) Bayesian statisticians will mention "Bayesian" on their CV. Frequentists will usually not put "Frequentist" on their CV, but much more typically the the area they work in (i.e., survival analysis, predictive modeling, forecasting, etc.). As an example, a lot of my work is writing optimization algorithms, which I'd guess implies you would say means I do Frequentist work. I've also written a fair chunk of Bayesian algorithms, but it's certainly in the minority of my work. Bayesian statistics is on my CV, Frequentist statistics is not.

(3) To an extent, what you've said in your question also holds truth as well. Efficient general Bayesian computation has more open problems in it than the Frequentist realm. For example, Hamiltonian Monte Carlo has recently become a very exciting algorithm for generically sampling from Bayesian models. There's not a lot of room for improvement of generic optimization these days; Newton Raphson, L-BFGS and EM algorithms cover a lot of bases. If you want to improve on these methods, you generally have to specialize a lot to the problem. As such, you're more like to say "I work on high-dimensional optimization of geo-spatial models" rather than "I work on high-dimensional Maximum Likelihood Estimation". The machine learning world is a bit of an exception to that, as there's a lot of excitement in finding out new stochastic optimization methods (i.e., SGD, Adam, etc.), but that's a slightly different beast for a few reasons.

Similarly, there's work to be done on coming up with good priors for models. Frequentist methods do have an equivalent to this (coming up with good penalties, i.e., LASSO, glmnet) but there's probably more fertile ground for priors over penalties.

(4) Finally, and this is definitely more of a personal opinion, a lot of people associate Frequentist with p-values. Given the general misuse of p-values observed in other fields, lots of statisticians would love to distance themselves as far as possible from current misuses of p-values.

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    $\begingroup$ So the answer to why it’s become more popular includes (1) it’s become more popular. Puzzled by that, but I imagine it’s just a matter of needing some rewording. $\endgroup$ – Nick Cox Mar 18 '19 at 14:49
  • $\begingroup$ @NickCox: my point is that it is more popular, but also it's popularity may be somewhat overstated. That is, the OP saw that Bayesian Statistics was on the CV of almost every professor at a sample of top tier universities. But that doesn't mean that every one of those professors only does Bayesian statistics. Another point on (1) was that I think there was a time when doing Bayesian statistics as your research area was very important for getting a top-tier position. I'm not sure it's as strict of a requirement anymore, but many of the professors you see now were hired during that time. $\endgroup$ – Cliff AB Mar 18 '19 at 14:55
  • $\begingroup$ Oh, I see your point. I was focusing on discussion of the "Is it because there is not enough room for advancement in classical/frequentist statistics?" and not so much on the "why is this happening?" $\endgroup$ – Cliff AB Mar 18 '19 at 15:23

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