Stat Assistant Professor

I'm not sure that this is universally the case. For example, at University of Florida Biostatistics, I would say that over 60% of the PhD students are international (last I checked). With papers and an MS from Duke, I think you can definitely get into a school like UFL Biostatistics or University of Pittsburgh Biostatistics and have a good shot at a place like UCLA Biostatistics, UT MD Anderson, or UPenn Perelman Biostatistics. The top-tier Biostat programs like JHU and UW may be very hard to crack (they also tend to be more theoretical/mathematical), but if you apply widely, I could see you getting in to a decent Biostat program.

If those classes are what interest you most, then I say go with them. If you decide to apply to PhD programs, you will have your Masters in Statistics (from a reputable department which will also work in your favor), so that signals to adcoms that you can perform well in Casella & Berger mathematical statistics and graduate-level Theory of Linear Models. Nobody will question your ability to handle more advanced mathematics if you have those plus a semester of real analysis. Having Advanced Linear Algebra and Numerical Analysis on your transcript will look great as well. In your statement of purpose, you can emphasize the mathematical nature of these classes to stress that you studied the underlying theory, not just how to apply numerical algorithms and linear algebra tools.

With your current profile, you could probably get into a lower ranked Statistics PhD program. I don't think your city college GPA will matter that much, especially if the classes are not in quantitative areas. But I would maybe briefly address it somewhere in your statement of purpose (one-two sentences) and point out the upward trend and your strong performance after you enrolled in a four-year program. However, if what you say is true about your undergrad institution not being very rigorous, then that is much more concerning than the fact that it is unknown. Above all else, you need to be able to handle rigorous mathematical statistics and statistical theory courses in the first two years of your PhD program, and you need to be able to pass qualifying exams on that stuff. Have you taken any proof-based classes (besides Real Analysis, which seems like it is a directed study rather than a class)? If you have only minimal exposure to advanced mathematics, then you will likely struggle in a Statistics PhD program (both the classes and passing the qualifying exams). If you want to maximize your chances of succeeding in a Stat PhD program, I would recommend applying to a handful of Masters programs (there are some funded ones in mathematics, and you can do a concentration in Statistics) where you can gain the requisite mathematical skills and then applying to Statistics PhD programs. If you are insistent on applying to PhD programs in the fall, then is there any way for you to take math/stat classes at a more rigorous university over the summer? Many R1 universities typically have two summer sessions. If it is not too cost-prohibitive for you, I would recommend taking Real Analysis as a class (not as a directed study) and Calculus-based undergraduate probability during one summer term, and then in the second summer term, taking proof-based Linear Algebra and undergraduate upper-level statistics. Depending on your performance here, you can then appropriately calibrate your list of schools to apply to.

If you interest is in epidemiology and infections diseases, it might be best to go for a PhD in Epidemiology or a PhD in Global Health rather than Biostatistics or Statistics (though I think many Epidemiology PhD programs require an MPH). An MPH or PhD in Public Health/Epidemiology would probably best serve your needs and teach you the applied statistics and methodology you need to know to conduct public health research without bogging you down in mathematical and statistical theory (if those are not of interest to you). If you still want to do Statistics, the only program I can think of which may be somewhat relevant to your interests is the Statistics PhD program at University of Washington -- UW Stats has a PhD concentration in Statistics in the Social Sciences: https://www.stat.washington.edu/academics/graduate/programs/statsocsciences

I read it from start to finish, but you can probably skip around after you've read the introductory chapters on regression and classification. As for supplementary materials, I did mainly search Google and Youtube. I found watching video tutorials to be particularly helpful.

You could certainly apply to mathematics PhD programs with your profile and the breadth of classes you took. Score well on the Math Subject GRE and you could probably get into a respectable math program. If that is your wish, then definitely ask for a recommendation letter from the professor who supervised your Masters thesis that you turned into a preprint. I don't think the admissions committees in Math departments separate the applications based on desired research field (nor do Statistics departments). You can mention individual professors with whom you would like to work in your statement of purpose, so your application might be passed along to them to take a look at and offer their opinion. But they won't be the ones accepting you - the admissions committee will be. One thing to consider about Math PhD programs is that the coursework would be quite different from ORIE or Statistics (i.e. in the first year of a Math PhD program, you'd have to take two semesters of Abstract Algebra, two semesters of Analysis, Topology, and Complex Analysis, and then in your second and third years, you have a bit more freedom to choose classes in your specialty).

These are very nascent fields (I've heard that even computer science conferences have difficulty finding suitable reviewers for papers on theory for deep learining) and so are fruitful areas for research. But since they are so recent, deep learning is not covered in The Elements of Statistical Learning (to the best of my knowledge -- there may have been a more recent edition of it than the one I read that contains sections on deep learning). I would also note that ESL is by no means exhaustive. The authors are frequentist statisticians, so the book only very briefly touches upon Bayesian approaches to the same problems in the book (e.g. nonparametric regression, classification, etc.). But I think as a "gentle" introduction to a variety of machine learning methods and models, the book is quite good. IMO, this book is best utilized as a basic introduction and should be supplemented by reading other tutorials and lecture notes/slides and watching video tutorials.

"The Elements of Statistical Learning" is a good book and I found it to be pretty accessible. If you have already finished the first year of your PhD program, you probably can just start reading it (and then refer to other references when you need to). I think it's a good idea to read this book from start to finish at a high-level (i.e. read it enough to understand conceptually what's going on rather than focusing on the nitty gritty technical details). Then you can refer back to parts of it later and read those sections much more carefully if they are related to your research. I never did any of the problems at the end of the chapter, but I don't think that would have helped much for research anyway. The best way to "start out" research is not to dive deeply into theory and technical details, but to get a broad sense of the field and then narrow the scope of your project (your PhD advisor should guide you to picking a suitable project that is not too ambitious and not too incremental but "just right" and doable enough to result in a paper or two). Reading through this book, watching tutorial videos, and reading review articles, lecture slides, tutorials, etc. are all great ways to learn the basics/high-level background of statistical learning. Once you start research, your advisor will probably give you a few important/"seminal" papers to read as well, and then it will make sense to delve into technical details, theory, etc.

I wouldn't say that any of your research interests are particularly "unconventional," but that aside, I think your list of schools is good given your interests, and I think you stand a good chance of getting into some of those schools with your profile. Scoring well on the Subject GRE would also help a lot at some of the top schools on your list. I can't think of any other schools to recommend off the top of my head, but a good idea when researching departments is to see if there are enough faculty publishing in mainly theoretical journals like Annals of Statistics, Annals of Probability, Journal of Theoretical Probability, Bernoulli, Stochastic Processes and Their Applications, and IEEE Transactions on Information Theory (other stat journals like JASA, Biometrika, JRSS-B also contain theory but these also tend to place a big focus on methodology, applications, computational/implementation aspects as well, whereas the other aforementioned journals are often mainly theoretical -- often times, there are articles published in Annals, Bernoulli, etc. that don't contain any simulation studies or applications on real data).

You could take a quick look through the publications and preprints of these faculty members and try to get a sense of which department is more appealing to you. If you are interested in applying mathematical tools from geometry and topology to statistics/ML and there are more faculty working on this at UW than at Princeton -- and said faculty are also publishing in top journals (like Annals of Statistics, Annals of Applied Probability, JASA, JRSS-B, Biometrika, IEEE Transactions, etc.) and top conferences (like ICML, NeurIPS, AIStats), then I would think that UW is a better fit than Princeton. But only you can decide which is better for yourself.

I don't think you would be a disadvantage in the academic job market if you had a PhD in Operations Research, particularly if the degree is from a school as prestigious as Princeton. Hiring committees (at R1's) care more about your publications and your ability to do high-impact work (assessed from recommendation letters and your presentations at conferences) than about what your degree is in. In theoretical statistics and ML, you definitely do use tools from pure math to prove theoretical properties of statistical models. Some subfields of stat/ML make heavy use of geometry and combinatorics. Others, like functional data analysis, need to use tools from functional analysis and Hilbert space theory. But statistics is still mainly an inferential field (making predictions and estimating unknown parameters and functions from data), and the emphasis is not on the most fundamental objects (like the probability space itself or the random variables/collections of random variables themselves) like in probability theory.

Princeton's ORFE Department could certainly lead to a great academic career in a Statistics/Math Department, especially if you work with Jianqing Fan who is quite famous and productive. However, one thing to consider is that apart from Fan, it seems as though the OFRE Department at Princeton focuses more heavily on probability theory and stochastic processes than UW, which seems to focus more on statistics and machine learning. While there is definitely overlap between these areas (after all, probability is the basic foundation of statistics), I would say that probability is more of a branch of pure mathematics and "fundamental science" than statistics. Every Statistics Department has a couple of probabilitists though. I would consider how much you enjoy probability theory and pure mathematics. If you are really into that, then Princeton OFRE may be a better choice. If you are more interested in statistics and machine learning (including the mathematical/theoretical foundations of statistical/ML models), then UW still may be the better fit.

Columbia U also has a very elite Statistics PhD program for sure (as does Duke). I think for Bayesian statistics specifically, Duke and Columbia are stronger than UChicago. When comparing Columbia with UChicago, there are more prominent Bayesian statisticians at Columbia. If you know that you are strongly in the Bayesian camp, this is something that should factor into your decision for choice of program.

I think Columbia has more prominent Bayesians (such as David Blei and Andrew Gelman) than UChicago. It seems like it is a good idea to trust your gut in most cases. UChicago is obviously a very elite program, but I would make sure they have enough faculty working on things you are personally interested in. Quality of life (e.g. living in Chicago vs. NYC) should also definitely factor into your decision. I would also add that there are other posters on this board who have turned down offers from elite programs such as Harvard, UPenn Wharton, etc. in favor of Columbia for reasons similar to yours (namely, a preference for the type of work done in the Columbia Statistics Department).

Congratulations on your excellent acceptances. You can't really go wrong with those choices, but I would say you should strongly consider Duke if you could see yourself being really into Bayesian statistics and computational stuff. There is definitely theoretical research going on there as well (particularly for Bayesian nonparametrics), but there is also a big focus on Bayesian methodology and addressing computational challenges at Duke. If you're agnostic about Bayesian vs. frequentist, then the other two might be better. It seems as though UChicago is the most theoretical of the ones on your list. Many talks I've attended by alumni and PhD students from UChicago seem to be solidly in theory (like proving risk bounds, attaining confidence intervals with the correct asymptotic coverage, etc.). So if you are solidly into theory, then that could be a good choice. Columbia seems to have a good balance of theoretical and applied/computational work, with some faculty who work a lot on statistical theory (e.g. Bodhisattva Sen) and others who work a lot on algorithms/methodology (e.g. David Blei). One other poster on this board was deciding between UPenn Wharton and Columbia Statistics, and they mentioned that they liked Columbia for being more applied than Wharton.

It's good to look at ML conferences as well, not just journals: ICML, NeurIPS, and AISTATS. It used to be that these conferences were far more prominent in Computer Science and not so much for Statistics. But nowadays, plenty of Statistics faculty also submit work to these top-tier conferences too.

A Masters degree can help for eventual PhD admissions to a solid mid-tier program in the USA (like OSU, Rutgers, or UF) if your undergrad math background was light, if your grades weren't the best in undergrad, and/or if your undergrad institution is very obscure. Agreed with the above poster that it would be easier to give you advice about your path forward if you provide more detail about your background. Of the two options you've provided, though, UMBC would probably be the better choice, as they have a ranked Statistics doctoral program (#69 in USNWR) and it seems as though their program is more "traditional" (with Masters comprehensive exams and PhD qualifying exams): https://mathstat.umbc.edu/graduate-programs-of-study/. They also have a Thesis option, although if you are planning to apply for the 2021 cycle, I'm not sure how much that will help your application. But as far as gateways to solid mid-tier doctoral programs, UMBC would certainly be the more promising avenue.

I saw that BU has just hired Yves Atchades as full professor, and he is a very strong researcher. If you were to go to BU and were co-supervised by Atchades and Luis Carvalho (say) *and* wrote two good papers as part of your PhD, then I would say you have a decent shot at a top postdoc. You could possibly get a top postdoc at a school like Duke in that case.

UW Biostat is certainly a very prestigious program, but is this capstone program fully funded? If it is not funded, then I am not sure if it is worth going into debt to use it as a stepping stone for PhD programs in the future when you already have three funded PhD offers. While a Masters from UW could very well help you get into more prestigious programs, I wouldn't say that BU, UMN, or OSU are so non-reputable that it is worth forgoing a funded offer from one of them in hopes of a "better" one in the future -- if your only admissions were to Applied Statistics PhD programs in regional/directional universities, I might consider the Masters option, but your current choices are not bad. If you want to 'move up' in academia or change your research direction, you can always perform well in your doctoral program and switch to something else during your postdoc. If you're aiming for industry, I don't think the school (BU vs. UMN vs. OSU vs. UW) will matter that much, although UW's location in Seattle might be slightly more helpful in getting data science jobs at big companies headquartered there.

Some programs are just very small and hence very selective. For example, NYU Stern's PhD program in Statistics (ranked #61 by USNWR) has only 6 PhD students total. I don't think the rankings are necessarily about program size. UPenn Wharton also has 5 PhD students in each cohort (for a total of 25 Statistics PhD students), but they are highly ranked, with many famous professors like Tony Cai, Ed George, Eric Tchetgen Tchetgen, Dylan Small, etc. It seems to me that the USNWR rankings mainly measure the perceived reputation of a program (i.e. responses to surveys sent to academic statisticians), and reputation is assessed in large part by how many famous faculty there are and what journals they are publishing in. Looking at Northwestern's departmental website, it seems as though only one faculty, Han Liu, is consistently publishing in the top statistics/ML journals and conferences like Annals of Statistics, Biometrika, ICML, and IEEE Transactions. A lot of the other faculty seem to publish in more 'niche' areas like education/behavioral science journals or bioinformatics journals -- these faculty may indeed be very good at that, but they may not be as well known to the statistics community as a whole, and the PhD graduates may be more likely to take academic positions in departments that are not specifically statistics (e.g. I saw on the Placements page that one of their alumni is now faculty at UPenn's Graduate School of Education).

I did not personally write any first-author papers during my PhD except with only my PhD advisor. Some students did collaborate with other Statistics faculty besides their PhD advisors. For example, I know this has happened if one of the professors taught a PhD elective and asked the students to do class projects. In some cases, the professor thought a student's class project was good enough to be extended into a publishable paper -- one person I know got a Biometrics paper and a good postdoc out of a class project. I would not say that collaborative research between PhD students and non-advisor Statistics faculty was very common though (from my experience). If you wanted to collaborate with other faculty and students besides your PhD advisor, you probably could have though, but you'd have to actively take the initiative to ask. I don't think most Stat faculty readily give research opportunities to students or postdocs whom they are not personally supervising, but it's possible that they might if you asked them. In my experience, it was more common for students to have two PhD co-advisors if they wanted to work with more than one professor.

When I was a PhD student in a Statistics department, I collaborated with a few people in the Agricultural and Biological Engineering department and I knew another who did some work for the Nursing department. You will probably need to seek it out on your own, though, or volunteer to do it. In my experience, the Graduate Coordinator or someone in another department will sometimes forward an email to the student listservs asking if any statistics grad students would be interested in doing statistical analysis, coding, plots, etc. This work will probably not count towards your PhD dissertation work but you will probably be listed as a third author on the paper that results from your work. A lot of Stat PhD students do not do this on their own volition though.

You can study machine learning in either a CS or a Statistics department -- indeed, there is a great deal of overlap between the two fields when it comes to machine learning, and a lot of the faculty will be cross-listed between Stat and CS/EE. That said, I would say there is a bit of a cultural difference in ML between Statistics and CS departments, in that CS people tend to be more focused on algorithmic aspects and predictive accuracy of point estimates (so models that work well in practice and that can be implemented with greater computational efficiency are preferred). Computer scientists seem to approach problems from more of an engineering perspective: how do we build a system that works to solve whatever problem we have? In contrast, Statistics people tend to be more interested in statistical inference (confidence/credible sets that quantify uncertainty of estimates) and theoretical properties of estimates like asymptotic/large-sample behavior, risk bounds, etc. There is of course still a great deal of overlap, with many computer scientists studying theory of machine learning and many statisticians becoming increasingly interested in scalability and computational complexity (which often involves borrowing tools from systems design, like distributed/parallel computing, etc.). But in general, it seems as though the underlying mathematical foundations and statistical properties are emphasized a bit more in Statistics departments, while the algorithmic aspects and empirical predictive quality are emphasized more in CS. Additionally, the admissions process for CS is quite different from Statistics. For CS, strong research experience is basically a requirement for getting into a reputable PhD program, and a slightly lower GPA is often forgivable in PhD admissions if you have excellent research experience and worked on papers with well-known faculty. Admissions in Statistics programs focuses less on research experience (though it is a plus) and more on "hard" numbers like GPA, grades in upper division math classes, breadth of math courses taken, and GRE scores. "Research potential" is assessed more often by letters of recommendation in Statistics, and there are a lot of students accepted into Stat PhD programs who have no experience with undergraduate statistics and little research experience, but a lot of academic experience in pure mathematics.

UF has several professors working on graphical models, including Kshitij Khare and George Michailidis. For job placements, I can tell you that this year, one of UF's fifth year PhD students got a tenure track Assistant Professor job at University of Minnesota and one got a job at Google out in California. And recent years have seen graduating students take postdocs at Columbia University, University of Pennsylvania, and Duke University, and industry jobs at Amazon, JP Morgan, Apple, and Siemens. Feel free to message me if you have any questions specifically about UF. The rankings of OSU and UF are about the same, and either one can set you up nicely for a good academic position or industry position if you play your cards right.

Agreed that the OP needs to retake the GRE and most likely needs to get a Masters degree to overcome the math grades and the fact that s/he attended a regional, relatively unknown school. But to become a professor at a regional school, you definitely don't need to get a PhD from a top 50ish school (you'll see faculty at these schools with PhDs from schools like Oklahoma State, Montana State, University of Central Florida, etc.). These types of institutions place far less importance on pedigree and research productivity than on things like teaching and likeliness to stay there long-term (so at these schools, having a PhD from a super-prestigious program can actually work against you in the hiring process, as they may assume you won't really want to go there). There's nothing wrong with working at these institutions if you prefer teaching to research and like the academic lifestyle but don't want to deal with as much pressure to publish, advise PhD students, etc. And even if you get a PhD from a lower ranked -- or even an unranked -- program, you can still get an R1/R2 job if your publications are good and well-respected (though, granted, the odds of attaining such an academic position will not be as good as if you attended a more reputable program and will be practically impossible without a postdoc or two from a more prestigious institution)... but it's not impossible to move up, provided your postdoc is productive and results in a few quality publications. For example, I saw that an alumnus of UT Austin's Statistics PhD program (ranked #50) is now faculty at UCLA.