kimmy

Also sorry OP that this thread has gotten distracted - I did an applied stats PhD at a top school, and got some exposure to admissions, feel free to DM me if you have any other Qs.

I'm sorry, I just can't let this stand unchallenged. It is complete nonsense to say that GLMs have had little impact on data science. Talk to any practicing data scientist and they'll tell you that a lot of the models actually being used in practice are relatively simple regression models. And survey sampling? That's a special case of weighting, which is heavily used in machine learning in the case of rare events (and also to increase algorithmic fairness). 
If all you're interested in doing is creating algorithms that do something faster or more accurately, sure, maybe you don't need a ton of statistical training. But, if that's all you're interested in doing, you're not really interested in being a statistician! Statisticians seek to develop tools for better data analysis, which includes quantifying uncertainty, carrying out inference, and improving model interpretability. It's impossible to do that without a solid grounding in the kind of old-fashioned statistics you look down your nose at.
Lastly, your conclusion that it is better to attend EECS/ORFE programs like MIT/Princeton because graduates from these programs have obtained positions in top stat departments is flawed. Top departments are often looking to find the smartest people they can hire, on the logic that they'd rather have a rock star who does something a little bit outside the norm than an "excellent-but-not-exceptional" faculty member who fits easily within the field. Sometimes, those brilliant people are in non-stat programs, but they're being hired because of their brains not because of their training. Indeed, if they were equally brilliant but had been trained in a stat department, they might be even more attractive candidates! Most people in EECS/ORFE programs will end up in those disciplines; entering such a program with the goal of entering a different field upon graduating is taking a huge gamble that you'll be so exceptional that hiring committees will overlook the fact that your research and training is unorthodox.
OK, rant over.

In addition to the above: I will also add that a lot of Statistics and Biostatistics programs do recognize the need to "update" the graduate curriculum to include more "modern" topics. Most statistics/biostatistis departments are aware of this and have either already done so or are in the process of doing so. So while you might still encounter a lot of 'classical' topics such as UMVUE, UMP test, James-Stein estimator, etc., the coursework often *does* give a splattering of more recent topics too, like high-dimensional regression, multiple testing with FDR control rather than FWER, etc.
But also, there is only so much that you can cover in classes. The subject matter of each class (e.g. probability theory, linear models, etc.) has enough material that you could easily spend a whole year or two covering subtopics in depth. You have to pick and choose what to emphasize and trust that once you give some basic foundation, the students will be able to learn other things on their own and pick up what they need for their own research.

Isn't that more due to the fact that MIT primarily only has people in either ML or high-dimensional statistics (and in this case I feel like the opportunity of working with Candes at Stanford or Wainwright at Berkeley is probably better than being at MIT), but there's more to statistics than these two fields: what if the person wanted to do something in causal inference or post-selective inference? MIT would clearly be not as great compared to other top stats programs. Additionally what makes a good EECS application is pretty different from what makes a good stats application: applying to EECS in ML usually revolves around having published somewhere in ICML or NeurIPS (sometimes even multiple times) as an undergrad, and comparatively grades/coursework really don't matter that much. 
 
Perhaps this is true in general about stats program curricula being outdated but if we are comparing Stanford/Berkeley to MIT this isn't really that true nowadays. People in the stat department who are interested in ML are encouraged to go take courses in optimization and information theory (which is what I am doing) because as you said, they are very useful. In fact one of the core courses at Berkeley gives a brief introduction to information theory because of how useful it is. But again, not everybody wants to do ML/data science/what-ever gets hyped up in the media nowadays and places like MIT EECS/Math or Princeton ORFE are really niche recommendations since they tend to lean very heavily towards a small subset of areas within statistics and have virtually no presence elsewhere. Also about your point for professorship, I know Berkeley gave out 3 offers for faculty last year, and 2 of them are for somebody with a traditional statistics background.
@kimmy sorry for the sidetracking but the people on this forum are pretty good at giving advice on applying to stats programs (probably because there are a few stats professors running around on these forums). I'd be somewhat more skeptical of any advice you'd receive here about applying to math or EECS (as to the best of my knowledge) because there aren't any similar such people on this forum and you should probably go look elsewhere for advice but do consider these options if that is something you are interested about. 

This guy has a history of posting... offbeat takes. (The last time I downvoted one of them, he actually went back through my history and downvoted every one of my posts).
If you want to be a statistician, it's probably a good idea to go to a stats program. While your advisor is important, so are your required courses/quals/classmates/seminars/etc.
Most of the profs he listed are pretty theoretical (makes sense they're in a math dept), OP seems more applied. For stat ML generally, they're a fine school but putting them at the same level as Berkeley/Stanford is a bit much.
I hear MIT's OR department is great, is pretty applied, although I don't think that's quite what you're looking for. Their EECS dept may be worth a look if you want to do that type of ML, it'd be a reach admissions-wise, but not completely crazy (though the advisors you'd be looking at are entirely separate from the listed advisors)

It depends on the math department. This situation is very rare. MIT and UCSD have good statisticians in math departments, but you don't have a profile to get into math programs like this. In the other end of the spectrum, University of Arkansas has some fine statisticians in their math program, and you could apply to a program like that. Texas Tech is another math department with statisticians, I believe. There are very few cases where people should be applying to math PhD programs if they want to be statisticians - so very few, that it is not generally worth mentioning. The comment was downvoted because MIT is not an important statistics program that needs to be mentioned nor is it a useful suggestion given your profile. 

An important omission on the above suggestions is MIT. MIT does not have a statistics department but it is possible to study statistics there through EECS, math, OR, or CSE track. The matter fact is that when you talk about the "hot areas" such as statistical/machine learning, inference algorithms, high dimensional statistics, MIT is as strong as (or is probably stronger than) Stanford or UCBerkeley. A list of "emerging superstars" there: Elchanan Mossel, Sasha Rakhlin, Philippe Rigollet, Guy Bresler, David Gamarnik, Ankur Moitra, and many many more. 
I'm surprised that this forum doesn't even mention MIT when it has one of the most powerful stats communities there. Not to mention that when you get into MIT, you virtually get into Harvard because you can have supervisors/collaborators at both schools and take any courses, joins any reading groups you like at both places. 

For OP - pick whatever programs you are interested in going to, irrespective of ranking, and apply to 5-10 of them. You won't get into all of them, but you'll certainly get into some. If you want stats programs with a decent applied group (which I'm guessing you do, based on your research), I'd particularly recommend Berkeley, UW, CMU. Maybe UW in particular, if you want strong biostats exposure.

You probably need to start by figuring out if you want to do a PhD in stat/biostat or math. While there are some differences between stat and biostat programs, they are tiny compared to the gulf between stat and math programs. From your background (coursework & research experience), you seem like a much better fit for (bio)stat than math, and would likely be competitive for a lot of very good stat PhD programs. 

3.85 GPA from an Ivy and a bunch of math classes including functional analysis, measure-theoretic probability, and stochastic processes, plus solid research exprerience. This is a very strong profile.
If I were you, I would apply to mainly top 15 USNWR Statistics/Biostat PhD programs. With strong letters of recommendation, I think you will be able to get into virtually all Biostat programs including Harvard and JHU. For statistics, you have a very good shot at UC Berkeley, UChicago, Carnegie Mellon, UPenn Wharton, Duke, etc. and I wouldn't be surprised if you also got admitted to Stanford too (I heard Stanford Statistics Dept is waiving the math subject GRE requirement this year for its PhD program?).