MathStat

Agreed that it doesn't matter.  You'll get good jobs regardless.  I will say that some of the companies that are pickier about applicants though, and even a top PhD will not be a guarantee of a job.  I have seen people from top 20 programs interview at FAANG who didn't know the basics of logistic regression, and at some of the top companies you really have to ace the interviews.  But if you have a PhD from any stats program, and you are knowledgeable, I don't think any position is out of the question.  I'm not sure how many people really get "research" positions though.  I think Facebook has a job called "research scientist" that a lot of statisticians seem to get, but I'm not sure how different it is from being a "data scientist" at say, Google, where tons of statistics PhDs are just regular data scientists.

From industry side, I currently work as a senior DS at a FAANG, and I work with many research scientists who‘ve earned PhDs from 60-80. Certainly there are also some from top programs like Harvard or Stanford but those are usually phds in humanities. 

Very interesting story. Maybe he is not dead-set on getting a PhD? Yale stats is actually very good. With guys like Harrison Zhou, Zhou Fan and Van Vu, I can even see one choosing Yale over Stanford when admitted to both. Not to mention the tremendous cost of money and time and the uncertainty of actually getting into Stanford (or even Yale itself) 2 years later. Sounds like a terrible decision. 

@stat_guy The "Wharton/Columbia/UChicago/Princeton" placements at Yale come from only 2 professors, one of which is Andrew Barron, a potential advisor I had considered myself when deciding grad schools. You should determine very carefully how active these two professors are currently, how motivated they are, and whether they are willing to advise you for the entire duration of your PhD (i.e. won't retire in a few years). As I mentioned above, Yale does have J Lafferty, a point brought up all the time both in favor of Yale and as a drawback to Chicago ("Chicago lost Lafferty, so it lost some of its value"), but is Lafferty actually actively advising students nowadays? Furthermore, many of the good placements came from David Pollard, but I think he must have retired by now.
Having 2 senior profs agree to advise you before you start is indeed very nice, so I completely understand your inclination towards Yale. If you are sure you want to do mathematical statistics, then go ahead. Chicago would indeed offer more diverse research options, including hot areas such as ML and, more recently, causal inference. For math stat we have Chao Gao who is recognized as a clear outstanding researcher and who likely will become tenured soon (definitely during your PhD time). Tengyuan Liang form Booth is also an excellent choice and he will also likely become Assoc. Professor soon enough. 
Chicago may not promise you a famous advisor from the start, but you can certainly have one later on, assuming there is a match in research interests. Your first year, you could work with a motivated younger professor, then potentially add a famous advisor later on. 
I encourage you to come to the Chicago visit day on Monday and ask us questions. I can answer questions through PM, as well. 

You are on good hands at Duke, best of luck. 

Responding to the statements in bold:
Finance companies recruit quants globally, not locally or regionally. I know people who have gotten full time offers for quant positions in finance from U Florida stats and UNC biostats. That should not be a deciding factor whatsoever in my opinion.
I disagree that Chicago's brand recognition is not as good as Yale. They're very comparable I think. Yale probably gets mentioned more in media, etc. because it's Ivy League. U Chicago has the 4th most Nobel prize winners out of any school in the world (by comparison Yale is 11th). I agree that brand recognition is not as important for a PhD. 
I would go to U Chicago. Much more to do, equal prestige, better department, etc. I don't really see where Yale has an advantage at all.
While I agree with @Stat Assistant Professor regarding the best way to evaluate is based on student outcomes, there could be a lot of self selection bias (such as what you are considering doing now).

As someone who chose Chicago versus UW (for phd not masters though), I'd also be curious to know whether there would be more tech opportunities for tech at UW (despite this info being useless for me at this point, haha...still, interesting to know).
As far as I know from my masters peers here, there are two options for classes at UChicago:
1. the hard path - take the phd -level sequences of applied stat and math stat (and probability, if you want). Stat 304 = distribution theory which is a core phd class taken during the first quarter is absolutely brutal and I heard many of my phd peers got less than ideal grades in it (I luckily was able to place out of it, by taking a Brownian motion class with the famous Greg Lawler, which was absolutely beautiful). Still, I know several people who chose this option, worked hard, got a very strong background (I personally think most phd classes, except STAT 304, are very reasonable), and were admitted to very good PhD programs. 
2. the less brutal path - take more typical masters level classes, which could include CS and ML classes from the CS dept or from the Toyota Technological Institute (which offers fantastic classes IMO). People who did this perhaps had a less stressful life, got very good grades, and still managed to get into great PhD programs. So it seems to me that this option is not necessarily worse for the purpose of stat grad school admissions. If you count the fact that you have a little bit more flexibility to take more CS/ML classes and prepare more for industry, this seems like the better option to me.
I think most if not all masters students here do pretty good summer internships in the summer between their two years. 
Also, while i think it would be hard to graduate in a single year (due to also having a thesis requirement in addition to the requirement of 9 courses), I think it is very doable and realistic to graduate in 1.5 years. There is a student I know of who did that and got a Data Science position at Microsoft (Seattle!!!). 
Also regarding tech jobs, I heard people can generally get them, but they turn them down for much better paid finance jobs here in Chicago. Again, can't comment if people here get *as many* good tech jobs as people at UW. 
Regarding applied/practical work, in addition to some classes that involve pretty useful class projects during the year (such as a course on "Multiple Testing", or some CS classes), we also have mandatory "consulting" projects, both for masters and phds. These involve working in a group of Phd and masters students to come up with a statistical solution for a client's applied problem (the clients here are generally PhD students from other depts needing further statistical support and analyses for their dissertation research; they usually come with already collected data). SO I think you can get practical experience here, despite the core courses being more theoretical. But perhaps you can get even more practical work done at UW, haha, and I'd again be curious about that. 
Hope this helps, let me know if you have other questions. 

Honestly from what I have seen of friends that landed tenure track positions, it all depends on you. You need to publish papers in top journals. 

If you don't feel super strongly about a topic, I'd personally lean towards choosing a school based on location, ranking, environment, etc.  One thing I would look at when choosing a department is the level of research and the journals they are publishing in and how that matches with your career goals.  If you want to be a professor, you want to work with someone publishing in top stats journals.  Some lower-ranked programs don't have many people doing this.
Some people I know had a strong passion when they went into grad school (eg spatial statistics, or clinical trials, etc) and chose the advisor that they came to the school specifically for.   This is a minority, in my experience.
A lot of people don't have strong preferences.  For instance, if you want a pretty "standard" job, like being a data scientist or working as a biostatistician at a medical center, it really doesn't matter that much what your specific dissertation was on.  Even for an academic job, some people just choose a good professor they feel they will be productive with.  And thus some people just sort of fall into their positions with their RAships, or based on taking a class with someone they like, etc.
Some people don't have a strong passion for a specific topic, but choose a hot topic that may land them the type of job they want.  If you want to be a researcher at Facebook or Google, studying network science/causal inference/deep learning might be a good idea.  Or some people might think genetics sounds cool and they start doing research in genetics.
Of course the topic you choose for your dissertation has some importance and you have to find something that is interesting enough to you that you enjoy it.  But I recommend not stressing too much about this if you don't already *have* a strong preference.  You'll never find the "perfect" research topic, and you will learn a lot by working on different topics and can always change directions during a post-doc or later in your career, too.  I wish I had spent more time earlier in my career just jumping into research instead of stressing about what I'm going to work about in the future.  But going to a department with a variety of options never hurts.

Assistant professor advisors have a lot of advantages. They want to get tenure, which means they are super-motivated to publish. Advising a student that lands a good TT job looks really good for their own tenure case as well. When I was a 3rd-5th year grad student, I felt I could really relate to the new assistant profs that we hired on a personal level. The student/advisor line was much blurrier.  
A few disadvantages: less name brand recognition, less experience, and possibly fewer connections. When I got my PhD, the only faculty who left our department in those 5 years was an assistant professor - not sure if that's an overall trend (assistant profs more likely to move than associate or full profs). Having to deal with an advisor that moves institutions is a headache but not insurmountable.

I went to a top 15 department and found the culture to be great. Everyone got along with each other (aside from a few minor riffs here and there), and we even organized events like department happy hours once in a while. We'd collaborate on homework years 1-2, study for the written quals together, etc.
By year 3 everyone went their separate ways with research but we all still remained friendly with one another, helped each other do mock prelim oral exams, mock dissertation defense presentations, etc. 
Sure, there was maybe some element of competition but at the end of the day we were ultimately competing against ourselves. Aside from 2 very strong candidates, the intersection between academic job applications was minimal as well.
Great experience overall where I went. Some departments may have a culture that could be viewed as "lame" or boring (i.e. everyone does their own thing and goes home, little interaction among students) but I haven't heard of any departments where the culture is super toxic and ultra-competitive.

how is harvard a good fit given your research interests? I feel like they're more into biostat/applied stuff..although Cynthia Dwork is there...
If you're into probability, deep learning etc, then berkeley and potentially other schools out of those 24 would be better fits. 
 
 

Are Harvard grads getting jobs at Google, Microsoft, Facebook, etc Research? I have not been stalking recently lol, but I cannot recall any examples (I wouldn't mind seeing some if you know any!). And the ones who get the top academic placements (aka berkeley and stanford TT professorships) seem to have worked in causal inference. If that is a strong area of your interests, then sure, go ahead.
I turned down Harvard (and had similar interests to yours and even a similar situation, haha), cause I thought there were only 1-2 people with similar interests as mine.
another bit of advice when you have to decide between almost all the top programs is to not get hung up on the top 2 ones that are ranked just after stanford. I think other ones you should also consider carefully given your interests are Columbia, UPenn Wharton, Duke, Yale (only if you wanna do pure math stat; imo they're some of the best at that). Make sure you review these carefully as well. 

how is harvard a good fit given your research interests? I feel like they're more into biostat/applied stuff..although Cynthia Dwork is there...
If you're into probability, deep learning etc, then berkeley and potentially other schools out of those 24 would be better fits. 
 
 

how is harvard a good fit given your research interests? I feel like they're more into biostat/applied stuff..although Cynthia Dwork is there...
If you're into probability, deep learning etc, then berkeley and potentially other schools out of those 24 would be better fits. 
 
 

how is harvard a good fit given your research interests? I feel like they're more into biostat/applied stuff..although Cynthia Dwork is there...
If you're into probability, deep learning etc, then berkeley and potentially other schools out of those 24 would be better fits. 
 
 

I think working with an Assistant Prof is probably fine. I have seen some TT faculty who had Assistant Professors as their PhD supervisors and who still landed many campus interviews for tenure-track positions. The most important things to consider when working with an Assistant Professor are:
whether their research is a good "fit" and whether they can help you to be competitive in the job market for academia or industry (either because they can help you publish in the top tier journals/conferences or because they have solid industry connections), and whether they are productive enough (by your department's standards) to earn tenure. If both criteria apply, then I say go for it. Besides, getting a TT position is the sum of many different parts, not just one thing. If your research is in a "hot" area that a hiring department currently lacks expertise in or if their job ad expresses special interest in recruiting applicants from your subfield, then I would think that you would enjoy certain advantages, regardless of who your advisor is. I also think that adcoms consider the strength of the recommendation letters too, not just whom they're written by.
It is a good idea to try to get your work noticed, though, so you can hopefully get a letter of recommendation from somebody who is influential in the field. One of my letter writers when I was on the market was from a pretty prominent name in the field, and this person was neither my PhD or postdoc supervisors... but I interacted with this person fairly regularly and they were familiar with my work, so they were able to write a very good letter for me. I believe that helped a lot.

@stemstudent12345
Sorry you're going through that. A bit of pragmatic advice: Just find a prof or two who support you, that's all it takes; cram the patterns of past quals. Not worth wasting your mental health on this, *really*. You'll be done with quals soon enough and you'll be able to pursue your own exciting and beautiful research, and from then on nothing else will matter. @Stat Assistant Professoris spot on. 

I'm sorry to hear that you are dealing with this. I don't really have much advice on how to rectify the specific issues with your department, but I do want to make a few observations.
1) It is true that international students typically have more extensive math backgrounds and are thus better prepared for the rigors of PhD coursework in statistics (e.g., it's commonly the case that a lot of international students have already taken classes at the level of Casella & Berger mathematical statistics, measure theory, etc., so in some sense, they already know the material in first-year courses). However, the gap between international and domestic students tends to narrow considerably by the third year, sometimes by the second. And by the time you start research, the majority of students are going to start out at the same level (i.e. not really knowing what they're doing).
2) If you make it past coursework and quals, then it's really the research that matters. This is what determines if you can earn your PhD -- and if you opt to stay in academia, this is what you will be judged on, not whether you earned an A or B in a core class (and if you're interested in teaching as LACs/regional comprehensives, then they will also judge your ability to teach and engage with undergraduate students). It is not unheard of for top-performing students in classes to struggle with research and take longer to finish, or for students who barely made it through quals to find their groove and excel at research. I've seen that firsthand at my own PhD institution where somebody who won "Outstanding First Year Student" struggled immensely with research and took a long time to finally finish. And other students who failed quals twice (failed first year exam once and failed PhD qualifying exam once) were still able to finish -- and even landed a TT faculty position later.  
3) Those of us in academia have all failed. Even if we didn't fail classes, we probably got papers rejected, grant proposals rejected, turned down for postdocs and faculty positions we applied to, etc. So if you're 'struggling' and faced with failure, you're definitely not alone.
I hope that you are able to resolve your difficulties. It is a tough situation to be in, and I am not really sure how to resolve it. Just know that if you can manage to get through the coursework, it's not all hopeless. 

The experimental physics professor seems like he would be able to write a more meaningful letter for you.

I don't have a clear answer to this. But I just want to comment that it can become extremely broad. For example, I recently discovered that Chatterjee at Stanford even works on quantum field theory! (https://statweb.stanford.edu/~souravc/qft-lectures-combined.pdf) It makes sense in that a lot of statistics come from physics. But eventually I think people just do things because they find them interesting.
 
 

Yeah, I can't imagine customizing letters of recommendation for every place. I have written a few letters of recommendation and always just sent the same one everywhere.
Even for faculty positions, my letter writers sent exactly the same letters to every place I applied to. I also did not customize the CV, research statement, or teaching statement. I did customize the cover letters, however (just FYI, for anyone who may be interested: the cover letters are especially important for faculty applications to PUIs because they really don't want to hire someone who will jump ship to a research university the second that opportunity arises). Those cover letters took awhile to write, because I spent at least 45 minutes looking through each department's webpages, faculty profiles, course catalogues, etc. 

In my PhD cohort of 9 students who finished the program, there were two of us that got TT positions (one is doing a postdoc now and the other 6 went into industry). Both of us applied to between 50-60 TT positions. Usually people focus their search on either research universities OR on PUIs. Some apply to both, but it's usually tilted more towards one or the other. In our cases, we only applied to jobs at research universities.
The number of TT faculty positions to apply to also depends on your profile. If you have several JASA/AoS/JRSS/Biometrika/Biometrics papers (including the applied stats journals like JASA-Case Studies & Applications or JRSS: Series C), you can afford to be a bit more selective -- but not *too* selective. But if there's a location that you absolutely cannot see yourself living in, you can probably safely exclude it from your list of job applications if your CV is impressive. This isn't the case with pure math, where even a PhD from MIT or Harvard doesn't preclude you from ending up at in a very remote location.  

To master a technique for me is very very hard. In fact, I often find that taking even a very solid class does not truly allow me to master a technique--in the sense that I can independently solve a problem using that technique. To give an example, I first learned the gaussian interpolation in a class in the context of Slepian lemma. Then I read Vershynin's book and learned it again, this time not only Slepian but also its extension such as Gordon's inequality. I even derived Gordon's inequality using interpolation as an exercise from the book.
Now when I see it again in the context of spin glass (Guerra's work on existence of free energy and upper bound), I stumbled as a total novice. I tried to prove these two theorems on my own without looking at the proof. Again, it proves to be quite a challenge and I just can't do it. So I studied interpolation fourth and fifth times. Later the monograph poses an exercise to use interpolation--again this takes me hours to finally solve on my own. You could imagine that to apply interpolation in a research problem in a nontrivial way could be much more challenging. So I still have a long way to go before I can claim myself a master of interpolation.
So in a sense, taking a class is as quick and efficient as it can get but in a way I also feel it is less "nutritious" a bit like junk food. Many classes (at my institution at least) feel like a guided tour around an amusement park. You see "prototypical arguments" of a lot of stuff in its simplest form, but it never gives you a feeling that you are "hitting it hard enough" by working out all the different variants. 
 
 
 

I often find that the best way to learn a new field/subject is to watch video lectures, read review articles and read select chapters from textbooks. So when I wanted to learn about variational inference, the first thing I did was watch a few video tutorials by David Blei and Tamara Broderick. After establishing this "baseline," I kind of just pick up on things as I go -- i.e. I just read the papers and try to figure out what the authors are doing as I go. This gets easier to do as you gain more experience and as you read more papers (in the beginning, I might annotate the papers a lot more). 
Realistically, when you are doing research, you won't know (or need to know) *everything* there is to know about, say, convex or nonconvex optimization. But you can pick up what it is you need as you go, and if you encounter something you're not familiar with, you get better at knowing WHERE to look and fill in those gaps.