Stat Assistant Professor

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. 

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. 

What was the curriculum in your "Applied Statistics" MS program? Depending on the rigor of the program, the Masters may not help your chances much (it wouldn't hurt them though). 
That said, I think CMU, Washington, UChicago, Michigan, and Duke are reaches, with the first four on this list being "high reaches." There is also a somewhat large gap in your range of schools -- you go from Duke to OSU. I think schools in the range Ohio State through Pittsburgh are reasonable to apply to for your profile, and you might also have a shot at some schools ranked between Duke and Ohio State. I would recommend applying to fewer of the first 6 schools you listed and adding more schools in between Duke and OSU.

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. 

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. 

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. 

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. 

1. In your SOP, you should definitely mention your research experience in preventative medicine, but say you are interested in delving more into statistical methodology that is *motivated* by problems in medicine. Also maybe ask one or two of your letter writers to mention that in addition to your research experience, you have solid mathematical training, having taken linear algebra and real analysis. 

2. This is my suggestion. Apply to 2 of the top 5 biostatistics PhD programs in the U.S. (Johns Hopkins, Harvard, University of Washington, University of Michigan, UNC-Chapel Hill) as your "reach" schools. I believe these programs are ranked in the top 15 combined stat/biostat rankings of USNWR. Don't bother applying to any Statistics (not biostat) programs in the top 15, since at this tier of school, your pure math background is not competitive when compared against other international applicants at these programs. 

Then apply to a combination of stat and biostat programs in the rank of 15-50 (but probably more stat than biostat), *except* for the Ivy League pure Statistics programs like Yale, Cornell, etc. Those are actually very difficult to get into and have just as high math expectations as the top 15 programs. I think the larger programs at public universities like TAMU, Purdue, Penn State are probably accessible for your profile. 

1. Yes, if you attended one of the top 3 universities in South Korea, you have a very decent shot at a top 40 Statistics PhD program in the U.S.A. A 3.8+ GPA from a school like Yonsei, SNU, or Korea University will make you very much "in the discussion." Since you also have some papers under review, that should also help your application (even if these aren't in statistics).
2. With your profile, you may be able to get into Statistics PhD programs ranked 15-40 (e.g. North Carolina State University, Texas A&M, Purdue, Penn State all seem like a reasonable bet for your profile). Above top 15 might be a little hard for you because your pure math background isn't as deep as other applicants from Asia -- these other students will likely have taken multiple semesters of analysis, measure theory, measure theoretic probability, sometimes classes like abstract algebra or Galois theory as well, etc. But you do have real analysis, so it's not completely hopeless for schools like TAMU and Penn State. I would apply to schools broadly from 15-50 maybe, and you can try one or two "reach" schools above 15. 
3. At this point, if you are already taking classes in the fall, then there's not much more you can do to improve your profile. Your GRE score and your TOEFL score are both perfectly fine. I would speak with your recommendation letter writers and ensure that they can write strong letters for you -- with a particular focus on "research potential" and mathematical maturity. If you can ensure strong letters and if you apply broadly (for you, I would mainly focus on schools ranked 15-40 by USNWR), I could see you getting into a decent program. As to whether you should apply to biostatistics programs too... are you interested in biostatistics and public health/biological applications of statistics? That should factor into your decision. But I've also heard that Biostatistics PhD admissions tend to be more difficult for international students because of limited funding (e.g. a lot of the NIH training grants are only for U.S. citizens/greencard holders). You could try a few Biostat PhD programs, but Statistics PhD programs will probably be easier for international students from prestigious universities in their home countries to crack.
If you go the Statistics route but are interested in biostat, you could always find a PhD advisor who does biostatistical applications. I know at the school where I did my PhD, some of the students in my department (Statistics) had Biostatistics faculty as PhD co-advisors. And even more theoretical departments like Stanford and UPenn Wharton have faculty who have a biostatistics tilt. For example, Susan Holmes at Stanford and Nancy Zhang at UPenn Wharton do a lot of stuff with complex biological data and statistical genetics.

Well, depends... if you're a domestic student, then you might be able to get one of those jobs without a PhD -- and sometimes with only a Bachelor's. I have a friend who has BS in Biochemistry but he taught himself programming/hacking/etc., and with the "right" connections, he was able to enter the field of data science. Now he has been working in the field for quite some time, and managing data science/engineering teams. So if you manage to get your foot in the door and obtain the right experience, your degree may not even matter that much.
But if you're an international student, then it is *much* easier to get an industry job in the U.S. with a PhD. This is because it is easier to get an H1B visa with a doctorate rather than only a Masters.

I don't think I would call any PhD program in Statistics particularly "easy." Many require a year of Casella & Berger, and the professors might make the exams very tricky. You have to practice a lot in order to learn how to be "clever" enough to pass the qualifying exams. That said, maybe somewhere like Stanford or UPenn Wharton would be considered "hard" because they start you out in measure theoretic probability and asymptotic theory your first year. But the students that they admit have typically already taken Casella & Berger-level statistics, linear models theory, etc. (and often, other advanced courses like stand-alone measure theory) before entering.
I don't think I would distinguish programs as "hard" vs. "manageable" vs. "easy." I would call some programs more "accelerated" or more "comprehensive" than anything else -- "accelerated" in the sense that what are second-year classes at most schools are first-year classes at these particular schools. And they may also be more "comprehensive" in that they might cover more material (e.g. some top biostat programs teach measure theory in their curriculum, but a lot don't). But it's not like students at other programs wouldn't be able to manage this coursework too if they were required to learn that stuff.

Well, depends... if you're a domestic student, then you might be able to get one of those jobs without a PhD -- and sometimes with only a Bachelor's. I have a friend who has BS in Biochemistry but he taught himself programming/hacking/etc., and with the "right" connections, he was able to enter the field of data science. Now he has been working in the field for quite some time, and managing data science/engineering teams. So if you manage to get your foot in the door and obtain the right experience, your degree may not even matter that much.
But if you're an international student, then it is *much* easier to get an industry job in the U.S. with a PhD. This is because it is easier to get an H1B visa with a doctorate rather than only a Masters.

If you are contemplating getting a PhD in Statistics and your profile is competitive enough *without* the Masters, then I would recommend just applying directly to PhD programs.
But if you do insist on going the Masters route first, then the Masters in Statistics (or in Math/Applied Math where you can take the stats classes) would be the best preparation for a Statistics PhD program. For one, it might save time later as far as fulfilling coursework requirements -- you might be able to place out of all the first year classes. I have a MS in Applied Math but I took 4 statistics classes in my MS program, including both semesters of Casella & Berger and the applied statistics classes. As a result of this, I decided to try my PhD department's qualifying exam upon arrival (after spending maybe hundreds of hours practicing old qualifying exam questions), and I passed it so I was able to skip all the first year classes. That saved some time as far as degree completion. 
But even if you do repeat the first-year classes (applied stats and theoretical stats sequences) once you enter a PhD program, you will be completely prepared because you will have seen the material previously. 

If you are contemplating getting a PhD in Statistics and your profile is competitive enough *without* the Masters, then I would recommend just applying directly to PhD programs.
But if you do insist on going the Masters route first, then the Masters in Statistics (or in Math/Applied Math where you can take the stats classes) would be the best preparation for a Statistics PhD program. For one, it might save time later as far as fulfilling coursework requirements -- you might be able to place out of all the first year classes. I have a MS in Applied Math but I took 4 statistics classes in my MS program, including both semesters of Casella & Berger and the applied statistics classes. As a result of this, I decided to try my PhD department's qualifying exam upon arrival (after spending maybe hundreds of hours practicing old qualifying exam questions), and I passed it so I was able to skip all the first year classes. That saved some time as far as degree completion. 
But even if you do repeat the first-year classes (applied stats and theoretical stats sequences) once you enter a PhD program, you will be completely prepared because you will have seen the material previously. 

Oh, I didn't realize you were from ISI. ISI enjoys a very strong global reputation, and adcoms will be familiar with the grading situation there. So pedigree is not an issue in your case.
That said, most Statistics PhD students from ISI have a Masters degree in Statistics from ISI, so it's hard to give advice to a math major from there -- though there are a lot of international students in Statistics PhD programs in the U.S. who studied pure math too, so I don't think that would be a handicap. It's just that I'm not sure how your profile would be compared to other ISI students who have actual BSc and MS degrees in Stat.
I think (?) you might have a chance at schools like schools in the range of University of Florida through Michigan State. MSU in particular has some great probability theory people. But it might make more sense for you to talk with an academic counselor at your institution to see how you stack up against your ISI peers who have BSc and MS in Statistics.

Hi @Riemannsum. If I am not wrong you have done Bachelor of Mathematics (BMath) and presently doing MMath(Master of Math) at the Bangalore center of ISI. @Stat Assistant Professor has already given you some very good advice. You should definitely approach some professors in stat-math unit who are close to you.  I have seen some past students from MMath (whose interest was mainly skewed towards probability) getting accepted at UNC, MSU for their PhD in Statistics. So, perhaps you can check that and can try to contact those seniors.(If you need more help you can message me). 

Most Stat PhD students from India are from Indian Statistical Institute or University of Calcutta, and occasionally some are from IIT (though in that case, they usually do a Masters in Statistics somewhere first). Since your profile is not "typical" for a Statistics PhD student in the U.S. who is from India, it might be hard to gauge your chances.
Does your program have a track record of success in placing its students in PhD programs in the U.S.? Have graduates from your program successfully been admitted to Statistics PhD programs in the U.S. in the past? The GPA may also need some context. At ISI, it is known that anything over 80 is considered very good. Is a 74-ish considered "above average" at your institution? 

I don't think I would call any PhD program in Statistics particularly "easy." Many require a year of Casella & Berger, and the professors might make the exams very tricky. You have to practice a lot in order to learn how to be "clever" enough to pass the qualifying exams. That said, maybe somewhere like Stanford or UPenn Wharton would be considered "hard" because they start you out in measure theoretic probability and asymptotic theory your first year. But the students that they admit have typically already taken Casella & Berger-level statistics, linear models theory, etc. (and often, other advanced courses like stand-alone measure theory) before entering.
I don't think I would distinguish programs as "hard" vs. "manageable" vs. "easy." I would call some programs more "accelerated" or more "comprehensive" than anything else -- "accelerated" in the sense that what are second-year classes at most schools are first-year classes at these particular schools. And they may also be more "comprehensive" in that they might cover more material (e.g. some top biostat programs teach measure theory in their curriculum, but a lot don't). But it's not like students at other programs wouldn't be able to manage this coursework too if they were required to learn that stuff.

It might be the case that there are a few Masters programs that are very competitive, like the ones that DanielWarlock mentioned (Harvard, Stanford, Princeton OFRE, and this may possibly be the case too with other small MS programs like Yale's). However, I am not sure that this is true in general. I think competitive Masters admissions is the exception rather than the rule. Even at 'elite' schools such as Columbia and University of Chicago, it does not seem to be very difficult to be admitted to Masters program in Stat.
A *lot* of Masters programs in Statistics and Biostatistics will admit anyone who has a reasonable undergrad GPA and GRE Q score, and who meets the minimum math requirements.

In that case, I think you could afford to aim a bit higher than the schools that are ranked lower on your initial list. I would recommend applying to more top 10 Biostat programs, like Michigan, Minnesota, UPenn Perelman. I think you have a great shot at those, and you might be able to get into UNC too. It might be more competitive  to get into JHU, but you can certainly try your luck.

In my (biostats) department at least, I'd say the vast majority of the money comes from grant money (e.g., NIH). You're right though that for larger schools where there's a lot of TA opportunities funding is pretty robust to economic shocks.

Funding for Statistics grad students is typically from tuition paid for by undergrads (and Masters students). In fact, I'd say well over 50 percent of the funding comes from the large survey courses (e.g. Introductory Statistics), which might have over 1000 students enrolled in a given semester. These classes are taught online for the most part anyway (with a possible small in-person component), and they have a lot of remote distance students even under 'normal' circumstances. Some "big shots" in the field also have a lot of their own grants that they can use to support PhD students as RA's. But most students are supported through TA. 
I think funding should be reasonably safe for Statistics. Not sure about Biostat, as there aren't typically undergraduate Biostat majors or undergrads taking biostat classes.

If that is the case, then I would recommend the OP look into Masters programs where they can take two semesters of NON-measure theoretic real analysis in their first year (along with the usual two semesters of Casella & Berger statistics and applied regression/design of experiments). If they have *no* experience with mathematical proofs, they should certainly not be taking measure theory. 
However, looking at the undergrad major for Statistics at UW, it looks like they actually do require a semester of Real Analysis as part of the major? https://stat.uw.edu/academics/undergraduate/major
However, the OP is a "data science and statistics" major so that might be different than the BS in Statistics.

No, as it stands, I think you would struggle to get into any top 40-ish programs. Even top 50 (e.g. Michigan State-type schools) are a reach for you.
Your chances would improve (a lot) if you got a Masters in Mathematics or Statistics, where you also take a few math classes, e.g. 2 semesters of real analysis, plus maybe one other math class (e.g. proof based linear algebra, numerical analysis, optimization).

I would think the last 4 schools will be pretty safe options and you'll get into a good chunk of the rest. Not sure about Stanford and Penn, but I wouldn't be surprised if you got into all the other programs.