MathStat

I just finished the notorious first year of coursework plus preliminary exams at the UChicago Statistics PhD program. Happy to report that I am still alive, and dare I say, excited to move on to research, despite the new set of struggles and uncertainties that will come hand in hand.
I do face the following issue now, which seems to be pretty common within US Statistics PhD programs - I recall, for instance, this very heated discussion from a few weeks ago, which did resonate with me a lot: https://forum.thegradcafe.com/topic/125581-school-suggestions/?tab=comments#comment-1058776870. Similarly to that post, I also felt that the first year coursework focuses on traditional statistics topics (in my case, linear regression, GLMs, overview of Bayesian methods, old-fashioned math stat, such as complete, sufficient, etc. statistics, UMVUE, minimaxity, admissibility, James-Stein estimators, and then some modern math stat, such as EM and variational Bayes algorithms, regularization methods, hypothesis testing and multiple comparisons), yet it misses some core courses needed for those who want to do modern ML research (guess I joined the dark side, too, despite starting off as a probabilist with interests in mathematical statistics). The particular courses I have in mind are optimization and statistical learning theory (and who knows what else I'm missing).
I am now trying to address this by taking a very strong learning theory course, yet I do not have time to wait for the optimization course which will be offered later. So as silly as this sounds, my question is, how does one efficiently self study new material relevant for their research, especially while balancing other courses, research, TAing, etc...? I feel that in order to gain the most thorough and solid preparatio,  one should take the past course materials and do all the grueling long homeworks, readings and so on, but then again, there are those other time constraints I just mentioned. I'd love to hear some advice from more experienced posters on how they pick up the skills needed for their research as they go. 
Thanks a lot!
 

Contrary to popular belief, I feel that 1st classes at my stats department uses very minimal real analysis. The prerequisite for almost any class is just linear algebra and calculus. You can literally know zero real analysis and do pretty well.
But a level of mathematical maturity is always assumed. It is mostly about problem solving rather than actual knowledge.
A CS major, if solidly done, should have absolutely no problem. A biology major will be more challenging (I'm not talking about "biologists" who are actually theoretical mathematicians or computer scientists in disguise). 
 
 

Any successful PhD student has likely struggled at several points in their training. My first year (Casella-Berger year), I barely managed a 3.5 while my peers were getting Mostly A's and A-'s (for the record, it's pretty hard to score below a B in grad school). After the first year, I was getting better grades than many of my peers who crushed me in the first year. The point of the PhD training is to tax you mentally so that you can start to mature mathematically.
I personally do not think grades or how well you do on the qualifying exam will make you a good researcher. It may be different in some old school professors' eyes, but I think most people these days view the qual / courses as a means to an end. At some point in your career as a graduate student, things will start to click together. And it's very possible you'll never see/use measure theory stuff ever again after taking it.
One of my peers was a bio major in undergrad, and ended up receiving the highest score on the theory portion of our doctoral exam. They had little/no previous exposure to real analysis. They are an extremely hard worker, so there's that. But all this to say, I think it's extremely possible for a bio / CS major to be successful in a statistics / biostatistics PhD program, albeit maybe the latter more than the former.

Great response by @Stat Assistant Professor. 
Casella Berger is already assumed knowledge for some top programs. But if you are admitted based on your pure math background (like yours truly) you likely won't have even cracked open Casella Berger or have taken a proper mathematical statistics course before coming in. However (and I hope this is not too strong of an opinion), Casella Berger presents math stat in a really outdated way. More modern and useful texts nowadays are from Van der Vaart, Lehmann and Casella, Iain Johnstone's Gaussian sequence model book, etc.. IMO Stanford does their math stat sequence in the best and most modern way. Their lectures and homeworks are online. The last part of their sequence, STAT 300C focuses on multiple testing, which is a very hot topic nowadays. 
Also, "hardness" of a program is a really subjective thing. We only discuss about the coursework and preliminary exam requirements above. For me, what also constitutes a big chunk of "hardness" is whether you'll be able to find a strong advisor that you like, whether you'll be allowed to start research asap etc, etc. 

I think @DanielWarlock has a point. MIT has a great list of faculties; one could research in statistics. Let me share my perspective here. 
Many statistics programs are getting a lot of attention because of the big data, machine learning, etc. However, one should note that there are so many programs that offer outdated curriculums. Honestly, who uses UMVUE, complete statistics? I haven't seen any of these in any papers I have read in top statistics journals published within 20 years. What's worse is that these programs still teach courses like survey sampling, generalized linear models(GLM), which had little impact on the data science's current emerge. I am not looking down on these two subjects, but one should note that these courses have almost nothing to do with the current data boom. In machine learning, you spend at most one lecture on GLM, but these outdated curricula still insist students take a full semester-length of GLM/survey sampling and other outdated topics. Now that I am working on so-called hot or emerging statistics fields, I feel my past education from statistics program was completely useless. Courses like Information Theory, Optimization, Graphical models that were not the core curriculum in the statistics program have become essential in modern statistics research. These are somehow more often taught in EECS/CS/Math departments.
Aligned with what I said, I think if one wants to have a better edge in applications in the IT industry or new methodological works in statistics journals, it would be better to choose EECS/applied math/ORFE programs like MIT or Princeton. Please take a look at the new Stanford/Berkeley faculties profiles, many of them were not trained in the Statistics PhD program. I think those on the level to get admitted to Stanford/Berkeley stats are on the level to gain admittance on MIT EECS/Princeton applied math. If not, programs like Georgia Tech IE/Upenn Applied Math have successfully yielded top students who acquired tenure track positions in top statistics programs. As far as I know, oftentimes, these programs require applicants to contact potential supervisor first, so with your background, I think it is worth considering. That being said, compared to the IT industry, biomedical applications are somewhat slowly accepting these new machine learning methods. I think this is why top biostatistics departments are still teaching outdated methodologies. In terms of the recent statistical methodological work, EECS departments like MIT have far more contributed than many other statistics programs, which cannot get out of their old fame. Also even at MIT, there are a lot of people working on computational biology.
Therefore, as @cyberwulf said, you would have to decide between traditional stat programs(many biostat programs and some stats) vs. data-sciency programs(stat programs like Stanford, Berkeley, CMU, Yale, Columbia, and CS/OR/applied math programs). Fields like genetics are highly computational, so even if you go to the latter program, the chance to work in biomedical fields is quite high. However, given the current training offered by biostat or traditional stat programs, I think the other way would be quite challenging. One way to distinguish these two types of programs would be to ask if the collaborations between departments(CS/applied math/OR) are frequent or have a lot of faculties with joint appointments. Having a separate Data Science institute or Initiative is also a sign of more data-sciency program. Lastly look into the curriculum they offer.

I could definitely see you get into either duke math or stat phd with your profile. I'd apply to duke math if I were you (several profs in the duke math department have cross appointments with stat, eecs, etc.; many of them do great ML research;  the department is also extremely supportive; the math phd cohorts are a little smaller than the stats ones; however the stat program is also great). 
And I agree with @StatsG0d, your lists are somewhat bottom heavy.

It should look something like this guy's webpage: http://www.travisfreidman.com/
Notice how he has his teaching philosophy, teaching goals, teaching competencies all very visible on his site. He also has a page for his teaching evaluations, including summary statistics, and he has the syllabi and course materials for the courses that he has taught. Your site should really sell your abilities as a teacher.
If you were to apply to a research university, you don't need to include as much (or anything, really) about teaching. A more "typical" webpage for someone seeking an R1 job would probably be something more along the lines of this: http://web.stanford.edu/~songmei/
 

6 total papers, I think... 5 of which were accepted/published (the other one under review) and one of which was in Annals of Statistics. 
As I said though, it isn't just about having some number of papers. It also depends on things like your research area and other factors beyond your control. If the search committee is, for instance, prioritizing applications from job candidates working in environmental/spatial statistics (say) and that isn't your research area, then you won't be hired no matter how long your CV is. If the department just recently hired somebody with very similar research as you, then they may opt to go with other job candidates who can "add something new" to the department. Search committees may also have their own preferences -- for instance, a member of the search committee might be really good friends with a job candidate's PhD or postdoc advisor, and they will forcefully advocate for that job candidate. It's stuff like that. 

The research records of people at these places do not have to be anywhere near if you were getting a job at a top 50 statistics department. An average person at these places will have one article in a journal like Statistics in Medicine or Bioinformatics, and some more applied papers, approximately. I'd highly encourage you to take an hour or two and look at the top 50 or so LACs' faculty pages. Also pay attention to the years of the publications. Some I've seen don't have many publications before starting but had papers in progress.  I think liberal arts colleges have a lot of incentive to get people doing applied research in things like environmental science, health, social science, etc because they'll get students interested in research. Harder to get a college student to help you with your Annals paper.

Yes, looking at the CV's of recently hired Assistant Professors at these schools is a good way to get some "baseline." It's not a clear-cut set of criteria for TT jobs, so you don't need [x] number of papers, exactly. It's more like if you have *at least* one paper in a top journal AND your research area is something that the department is interested in (so for example, a probabliitist with a very prolific record won't get an interview if the department isn't interested in hiring a probabilitist), then you will usually make it past the initial cut where they trim down all the applications into a set of 20 or so that they look at more carefully.  And the more papers you have in top journals, the fewer *total* number of papers you need (for example, an Assistant Professor at UPenn Wharton who joined the department in 2019 had "only" four papers, but three of them were in Annals of Statistics).
I don't think working with an Assistant Professor is necessarily an issue. There was one job candidate on the job market in the 2019-2020 hiring cycle who got like, 20 interviews, and her advisor was an Assistant Professor. She also got offers from UIUC, UNC, UFlorida, UMinnesota, Columbia, and probably others as well.

I agree, nobody cares but Stanford. Not even Chicago, Berkeley, UW, Columbia etc etc. 
Although as a funny story, one of the Duke stat faculty told me they like to see the score if you wanna do research in math stat. Duke also used to say on their website not to bother with sending the scores as they won't look at them. 
Gotta love academia
 

Stat Assistant Prof answered some of your non-teaching questions here: https://forum.thegradcafe.com/topic/116685-good-productivity-benchmarks-for-a-strong-research-advisor 

I have a variation on the original question.  Some of the posters seem very knowledgeable in this area.

If someone attends a top 10 stats program what do the schools look for if the applicant wants a tenure track   research  based assistant professorship at an R1?
Do teaching skills  matter?
 
Is there any way to bypass a postdoc these days and go straight into an AP?  Is there any way to quantify how many publications and in what journals are needed for the AP?  How much do LORs really matter?   
 
 
 

Some of OP's questions seem like they might be answered with the slides and video recordings from eCOTS's workshop on preparing for teaching-focused faculty positions; here is the website to access that: https://preparingtoteach.org/agenda/ (there was recently a review of this posted via Sara Stoudt and Mine Cetinkaya-Rundel, posted here for a quick summary: hathttp://www.citizen-statistician.org/2020/06/preparing-to-teach-2020-what-did-we-learn/). That said, they seem to largely agree with our experienced posters, so this may not be worth your time.

The top schools on the USNWR list look about right to me (NYU Courant, UCLA, and MIT). I would suggest you look at more than only rankings. Make sure there are actually enough faculty who are: a) doing research in your area of interest, and b) who have solid placements for their advisees. Are they placing their former students into top postdocs? If the school is a top-tier one like NYU, UCLA, MIT, Princeton, etc., the answer to part (b) is assuredly "yes." But beyond that, I would make sure there's a big enough group of researchers there. Some programs might be stronger in some area of applied math like PDEs/fluid dynamics or numerical analysis/optimization than others.

Some people on this forum seem to know people who do things like this, but I'll just give my experience/knowledge with tech companies.
If you're doing deep learning or something more CS-related, there are probably many more such opportunities. The ML/Statistics research group at Microsoft has 9 people, and many of them are not statisticians: https://www.microsoft.com/en-us/research/theme/machine-learning-statistics/. Google to my knowledge does not have statistics researchers outside of their normal data scientists (who do things that you might consider research?).  Facebook research does seem to have a bigger core data science team, which is more research-oriented.  The biggest key to being hired is likely having done the right type of research (deep learning, causal inference, networks, something that they have a need for) and having impressive publications.
The compensation is going to blow away anything in academia. Entry level data scientists with PhDs start at these companies at $200k+ total compensation.  I imagine researchers make at least that.  It is my impression that there are not enough of these positions for it to be a definite career path.  There are hundreds of people with PhDs from top 20 statistics programs just working as regular data scientists at these companies.

Of course they should first of all think very well which program they really want to attend.
It is possible to experience strong second doubts before starting your program, especially when you had several fantastic options or in circumstances where your decision was constrained by other factors which made it very difficult. furthermore, as horrible as this sounds, i think it is quite common that current students start disclosing more of the "ugly sides" of your future program after you have already committed and it is too late to do anything (as opposed to the visit day, where they only reveal positives). from my experience, these profs understand it is such a difficult and life-changing decision and I think they would truly want you to end up at a place that fits you. I also have the cynical belief they do not care that much about you (just yet) so it's not a big deal if you say you will attend a program, and then back out. I think it would be possible to first discreetly ask the other department whether they would take you back, then plan your next steps accordingly. 
 
edit: sometimes, departments decide to offer you more money right at the last minute, during the weekend before april 15th, after you already committed to a program. this puts you in a very difficult spot and you can imagine that, if you decide to be ethical and stick by your initial choice, you would still experience second doubts creeping in...

Do people on the forum have insights as to research at MSR, Google, FAIR and the similar industry groups? My department (statistics at a top 10 school) does not really send anyone to such jobs and so I do not have much information about them. I want to spent at least one summer testing out the waters.
How does one go about getting a research scientist internship at these firms? Is it primarily via a referral from one's advisor or department?
How does the compensation look vs academic jobs (Principal Researcher at MSR vs an associate prof)?
How is the research different vs academic jobs?

@incomingstatsPhD, have you tried contacting the program you are regretting turning down? if not, i think you should do it like RIGHT NOW, and just explain your reasons honestly. it's still may, perhaps there is still time to revert this. you'll never know if you don't try. 

I think you are going to see another "post-doc pileup" similar to what happened in 2008-2010. Before that time, most PhD grads in stat & biostat seeking academic positions didn't do postdocs; then, for a couple of years, a ton of grads were pushed into postdocs by the lack of faculty positions and when hiring started again they had much better CVs than the fresh grads they were competing against. So, for the past 10 years, it's been pretty tough for PhD grads without a postdoc to land a tenure-track position.
I expect things to trend even further in this direction over the next several years: it may become virtually impossible for new grads to get academic positions without a postdoc, and multiple postdocs may become much more common. We may start looking increasingly like the lab sciences, where it's rare for new Assistant Professors to be hired without 3+ years of postdoc experience. 
However, there is one countervailing factor that may work in (bio)stat's favor. Interest in data science was already high pre-pandemic, and I expect that even more people will become interested in statistical modeling and data analysis due to this experience. As a result, funding for stat/biostat hiring may be one of the first to return to pre-COVID levels simply to respond to increased demand for both data-oriented teaching and research.

The job market for postdocs should remain somewhat robust (hiring is still allowed at a lot of schools as long as it’s funded externally, e.g. through grants). But the academic job market for tenure-track positions will be a lot tighter for a few years. For this reason, I would recommend anyone trying the TT job market to give themselves a deadline on how long they are willing to be a postdoc before moving on.
I am actually serving on the hiring committee for my new department this fall (although most have instituted a hiring freeze for this upcoming AY, a few places are still hiring), so I will be able to give more insight into hiring from “the other side” by next spring. However, based on personal experience and what I’ve observed from other job market candidates that I was competing against:
For Stat and Biostat, having a strong publication record is the most important thing for getting shortlisted for TT jobs at research universities. Having at least one paper in JASA, JRSS, Annals of Statistics, Annals of Applied Statistics, Biometrika, Biostatistics, and/or Biometrics seems to help a lot. If you are in a niche field like statistical genetics, then publications in the top field journals like AJHG or Nature Genetics will matter more. Thus, if your aim is to obtain a postdoc before trying the TT market, it is very important to choose a postdoc supervisor/lab group that has a strong RECENT track record of publishing in quality journals and a strong RECENT record of obtaining external funding and placing postdocs/PhD students in good academic positions. That way, you will also be able to gouge if they are working on topics that are of current interest to the stat/biostat community. It is also extremely helpful to get letters of recommendation from renowned professors. If someone on the hiring committee knows your PhD/postdoc mentor or one of your letter writers, it can go a long way. That’s also why it is advisable to do a postdoc at a prestigious institution if you can. Note that this applies mainly to jobs at research universities. It’s a little bit different for jobs at primarily undergrad institutions and Masters-only regional schools. Here, teaching experience will be more highly valued, and your job application needs to demonstrate that you understand their teaching mission.

I personally do not think average grades in multivariable calculus and linear algebra are so dramatic. 
For what it is worth I got B+ in multi because I couldn't do the tricky double/triple integrals fast enough during the midterms. This did not affect my phd admissions but granted I had grad level math courses with As to make up for it. 
Linear for some is also a tricky course the first time you see it. If I hadn't struggled with it before in high school I would've also gotten a B in my first semester linear class. I would say it is perfectly understandable to mess up the math classes in your first year if you didn't have exposure before. 
" My grades in stats, machine learning and CS classes have all been A/A-'s and one or two B+'s. " <- that is very good. 
The nice thing I notice about the United States is the culture of "second chances". The postdoc who helped me immensely to develop beautiful undergrad research also messed up his linear/multi and other math classes in undergrad. He said he had mostly bad grades during his math BS at UW. He stayed for a masters to fix his background, then did very well in his math phd and was able to secure a postdoc at duke with one of the best probabilists in the world. There are tons of similar examples from stat, including a stat professor I had at duke who climbed her way up from not prestigious undergrad and masters to phd at UFlorida, then postdoc at CMU, then tenure track at Duke. There is hope @L2norm! Many established and strong researchers were able to not let their  "humble" beginnings define their future. The issue is that all that I know of are American citizens...so i can't really comment about internationals. 
The question is: since your gpa is rather low but your math/stat/cs course grades are pretty good since you only have 2 Bs, it means you messed up most of your humanities/social sciences classes. Do stat programs really care about this?

I personally do not think average grades in multivariable calculus and linear algebra are so dramatic. 
For what it is worth I got B+ in multi because I couldn't do the tricky double/triple integrals fast enough during the midterms. This did not affect my phd admissions but granted I had grad level math courses with As to make up for it. 
Linear for some is also a tricky course the first time you see it. If I hadn't struggled with it before in high school I would've also gotten a B in my first semester linear class. I would say it is perfectly understandable to mess up the math classes in your first year if you didn't have exposure before. 
" My grades in stats, machine learning and CS classes have all been A/A-'s and one or two B+'s. " <- that is very good. 
The nice thing I notice about the United States is the culture of "second chances". The postdoc who helped me immensely to develop beautiful undergrad research also messed up his linear/multi and other math classes in undergrad. He said he had mostly bad grades during his math BS at UW. He stayed for a masters to fix his background, then did very well in his math phd and was able to secure a postdoc at duke with one of the best probabilists in the world. There are tons of similar examples from stat, including a stat professor I had at duke who climbed her way up from not prestigious undergrad and masters to phd at UFlorida, then postdoc at CMU, then tenure track at Duke. There is hope @L2norm! Many established and strong researchers were able to not let their  "humble" beginnings define their future. The issue is that all that I know of are American citizens...so i can't really comment about internationals. 
The question is: since your gpa is rather low but your math/stat/cs course grades are pretty good since you only have 2 Bs, it means you messed up most of your humanities/social sciences classes. Do stat programs really care about this?

What are the job placements like for the schools you mentioned? For industry, it probably makes no difference. For academia, having to take these courses may be helpful in that they allow you to sharpen your proof skills, and you pick up on certain techniques from them that you can use repeatedly in your research (splitting the expectation ftw). But if you read enough papers carefully, you can probably also pick up on "standard" proof techniques.
For academic hiring at research universities, it's most important that your *research* is prolific and at least some of it is cutting-edge (i.e. getting published in the top journals or top machine learning conferences), not the content or grades of your coursework.  
Anyway, my two cents: Lehman and Casella is a very classical text but a lot of the material in it may not be very relevant to most modern statistics research (for example, L&C gives a *very* rigorous treatment of UMP tests, admissible estimators/tests, etc., which isn't a popular research topic now). I guess it's nice in that L&C has a lot of material on things like James-Stein estimation that was one of the earliest shrinkage methods (before lasso and all the sparse regression methods). But is it really necessary to know the risk/minimaxity properties of these kinds of estimators in great detail? I'm not sure.
As for probability theory, I definitely think it's good to be able to understand notation for the Lebesgue integral and know basic inequalities (e.g. union bound), but if you're a statistician and not a probabilitist, you may be able to get away with only the basics. I believe that at UC Berkeley, PhD students in Statistics do not even need to take measure-theoretic probability (they can instead take only the Applied Statistics and Theoretical Statistics sequence), and their PhD graduates seem to get along just fine.

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.