Stat Assistant Professor

It really depends how prestigious the big state school it is -- the adcoms will set the bar much higher for your application if you went to say, Oklahoma State than to a school like UC Berkeley or Georgia Tech. But notwithstanding that, I think with the B that you received in Graduate Level Math Stats will make it extremely tough to get into the majority of the schools on your list. I would probably cross Stanford, Berkeley, Penn, Columbia, Duke, Yale, Washington, and JHU off your list, as these do not seem realistic. I think you definitely need to aim lower for Statistics and possibly Biostat as well.

I'm not aware of any Masters programs in the U.S. that give funding to international students (although I'm sure that there might be a few that exist?). Is there any way that you could complete a Masters degree in your home country at a highly ranked university? That would help your case a lot. Unfortunately, as things stand, I think that at a lot of schools in the U.S. would immediately reject your application, just because of the sheer volume of applications that already come from the top 15 or so schools in China, the top 5 or so schools from South Korea, and ISI, University of Calcultta, and a few of the more well-regarded IIT's in India.

You didn't mention what the prestige of your university is. For international applicants, the prestige of their undergrad carries a huge amount of weight. Most of the top programs could fill their incoming class with *just* students from Peking, Tsinghua, Fudan, Seoul National, KAIST, ISI, etc., if they wanted to. So if the university is not well-known to the admissions committee, they might just automatically reject the application. The only way I've seen international students from less prestigious schools getting admitted to Statistics PhD programs in the U.S. is by first doing a Masters degree at a more prestigious school (either in their country or in the U.S.)

I think your list is rather top-heavy, and some of those on your list are *very* difficult to get into, unless you have a superstar profile with tons of advanced math classes (e.g. UPenn Wharton only admits 5-6 new students every year... and a lot of the time, 4 of those will be international students). Admissions can also be a bit unpredictable, and ranking does not always correlate with admissions chances -- there are other posters on this board who had similar profiles to you who reported getting admitted into TAMU but rejected from UCLA. Yale Statistics is also very difficult to get into even though it's USNWR ranking isn't as high as say, Stanford. I would take a closer look at those schools and trim down the list of schools from the top tier to ones that really seem like the best fit. You can apply to a few of those, but I would add some bigger programs like NCSU, ISU, Purdue, and UIUC. It may not hurt to apply to some schools like Rice, UConn, and FSU too to be safe.

It's often helpful to study worked out examples and to use WIkipedia, Wolfram, online course notes, etc. to fill in any terminology you may have forgotten or haven't seen before. Most people forget details after they've taken a class and need to refer to online resources or textbooks to help them in their research (apart from WIkipedia, 'standard' linear algebra references include the Matrix Cookbook or "Matrix Algebra from a Statistician's Perspective"). I would look up mathematics basic qualifying exams on advanced linear algebra that have solutions (e.g. UCLA Basic Examination for incoming math PhD students) and try to understand what they did. The more exposure you have to it, the easier it will be to do it yourself. EDIT: Here's a set of qualifying exams that have proof-based linear algebra examples: https://clas.ucdenver.edu/mathematical-and-statistical-sciences/previous-linear-algebra-exams-and-solutions There are many others posted on other departments' websites.

Actually, I think your strong mathematics background, your excellent subject GRE score, and your prestigious school all make you a *more* attractive candidate to Statistics departments. This is especially so at some schools like UC Berkeley Statistics Dept where they make you submit a separate document listing ALL the advanced math courses you have taken, grades earned in those courses, and the textbooks used. You don't need to be concerned about the lack of a specific research area, lack of research experience, or the fact that your LORs are only from math professors. There are plenty of PhD students in Statistics who took no probabillity/stat courses prior to enrolling (which you have done) -- they only took pure math classes. The very top-tier schools (Stanford, Chicago, Penn) are always tough for anyone, but I think you should be able to be admitted to at least a few of those on your list (definitely schools at the level of ISU, Purdue and UCD). I wouldn't be surprised if you got into somewhere at the level of UWisc or higher.

I would add to dmacfour's comment that apart from academia, a PhD is useful for getting jobs as Research Scientists, positions which are typically not available to those with only Masters. The department where I earned my doctorate has PhD grads employed as research scientists at Amazon, Siemens, etc. working in areas like machine learning and AI. The PhD trains you to be a researcher. If you just want to learn some current machine learning methods and get a job quickly, then a Masters is the way to go (and sometimes that isn't even necessary -- I have a friend who only got a Bachelor's in Biochemistry but then he self-taught himself all the programming and machine learning tools to break into the field of data science). These jobs can also be interesting and you can learn new methodologies/programming hacks/etc. on the job.

In the field of Statistics, you are typically accepted by the department and then you choose an advisor after you pass quals. You aren't accepted into a professor's lab or research group, so it's not nearly as essential to reach out to professors. Many people who get admitted to the top programs in this field never reached out to individual professors. I would proceed with caution. If you're going to do it, you had better make sure you *really* know what you're talking about (i.e. you actually read one of their papers and you can discuss it at a somewhat sophisticated level). If you have credible research experience that aligns with the professor you're interested in working with, then I think it's fine too... not strictly necessary and I'm not sure how much it will affect your chances in admissions, but if you can have enough familiarity with the professor's work (and more broadly, their research area) to discuss their research, then maybe it's okay.

It's worth noting that most students in Statistics PhD departments don't even take a full semester or year of stand-alone measure theory/abstract integration/functional analysis, UNLESS their PhD advisor recommends it (or unless they are just doing it for their own personal edification). In the department where I got my PhD from, the professors who specialized in Markov chain Monte Carlo theory *might* recommend their PhD advisees take functional analysis (since they need to work with Hilbert spaces and operator theory), and I'm sure the profs who do theoretical research on stochastic processes would also recommend this to their students. But just about every other PhD student I know only learned measure theory in their PhD probability class.

If you think you want to conduct research more on the probability theory side rather than statistics, then take the graduate analysis sequence. But if you are genuinely interested in Bayesian statistics and you think you might want to conduct research on it, I think that this sequence would be much more worth your while. Assuming your application is already very strong (e.g. other math classes, including undergraduate real analysis), I don't think it's really necessary to have a very deep knowledge of measure theory/abstract integration prior to enrolling in a Statistics PhD program. They usually teach you the measure theory they want you to know, and it's usually not even necessary to take a whole stand-alone class on it (unless your specialization is in probability theory rather than stat).

UF awards the Master of Statistics degree to those who obtain a "Masters pass" on the First Year Exam and who complete a Masters project. A 3.0 GPA is also needed to stay in the program but that is standard across all departments and grad schools (two people one year were asked to leave the program without a MS since they couldn't keep their GPA above 3.0). I think almost all schools in the USA give you the option of getting a Masters along the way, either automatically after passing written qualifying exams and finishing required coursework, OR after all Masters requirements have been completed and an additional written Masters report/project is done. I would be surprised if there are any programs that explicitly forbid this "exit with a Masters" option, but maybe I'm just personally not aware of any.

A Masters in math should be fine for admissions to most PhD programs in Statistics too (I know many people who took no stats classes prior to enrolling in Statistics PhD programs but who obtained Masters in math). Several PhD students/alumni in my department fit this description (MS in math -> PhD in Stat), including one alum who is a professor at Duke and another who is a professor at University of South Carolina. But I would say only do that if you are truly interested in math. A Masters in Statistics can also be used as a stepping stone for a PhD in Statistics, but if your undergrad math background was light, you may need to take a few extra math classes in your Masters study (e.g., real analysis) to better your chances for PhD admissions. Agreed with above posters that programs like Masters of Applied Stats, Masters in Professional Studies of Stats, Masters in Data Analytics, or Masters in Data Science are unlikely to be helpful for PhD admissions.

A lot of students enter PhD programs (and other professions like medicine, law, etc.) for the perceived social status, because they were "good at school" and they figured the PhD program would be an extension of undergrad, and for the job prospects. I do think that the attrition rate does tend to be higher for those students in most disciplines, including Statistics. I think it's okay to want to do a PhD for the improved job prospects and the status (admittedly, in some fields like CS and statistics, having a doctorate *does* confer higher earning potential... and if you're more picky about the areas you want to work on, then having a PhD is helpful). But one should be cautioned about a number of things: - having a PhD =/= automatic respect for your opinions. As with anything, respect has to be earned, and reputation takes many years to build up. A PhD makes you a mini-expert in a very specific area of study, and people will rarely assume that this makes you an authority on other matters. So you should definitely do it because you personally want to do it for your own fulfillment, not because you think others will have a much higher opinion of you. - be aware that it is a lengthy time commitment and that there is high opportunity cost. So unless you can tolerate the idea of spending 4-6 years on it, earning $30k or less, you might be better off getting a Masters and/or working full-time. - the PhD is ultimately about producing an independent researcher. Grades don't really matter in a PhD program, as long as they are above a 3.0 GPA (in order to keep your funding). Moreover, research is not at all like studying for a test. It's about repeatedly trying different approaches to tackle a problem, encountering numerous failures and setbacks, and learning when to give up and move on. Even after you've completed research and written manuscripts, it's likely that some or all of your papers will be met with rejection from journals or conferences. For the straight-A students who are used to acing all their classes and being the top student, a PhD can therefore be very demoralizing and disorienting. That's why I think it's a good idea for bright students to know what they are getting into and to be mentally prepared for failure and rejections. After awhile, you just get used to it and learn how to keep going in the face of failure/rejection, but for students who haven't encountered this a lot before in their academic careers, it can be very disheartening.

I think many reputable programs put you through pretty intense theory classes for the coursework portion of the program, especially in the second year... including many of the schools on your list. But once you are done with courses, the PhD research needn't be super theoretical. The department where I earned my PhD focused on theory heavily for courses (including two semesters of probability theory -- though there is a possibility that it may be condensed to one semester beginning in 2020). Even so, there was one PhD graduate this year wrote their thesis on statistical modeling of power theft detection and power demand forecasting in the smart grid. And there was one from last year whose thesis was on Bayesian calibration for near infrared spectroscopy. I imagine if there is a big group working on statistical genetics, you can find enough faculty who focus on applied/computational aspects instead.

In that case, the OP would be a very competitive candidate for PhD programs if s/he took both Math 112: Introductory Real Analysis and Math 114: Analysis II. I think just taking Math 112 might be sufficient for being in the discussion for admissions, but adcoms may look favorably upon having studied basic measure theory/Lebesgue integration. In my PhD program, we had to take basically a whole semester of measure theory/abstract integration, but a lot of stat programs condense this into the first few weeks of a one-semester Probability Theory class before diving into the classical probability theorems (Fubini, Fatou lemma, etc.).

After looking at the course websites for Math 212a and Math 212b, I would agree with the above poster that these are not necessary for statistics Masters students. It seems like Math 112 (Introductory Real Analysis) at Harvard would be the most appropriate real analysis class for Masters students who are interested in applying to stat/biostat PhD. It seems that only one semester of Math 112 is necessary too, since they seem to cover the whole analysis sequence in one semester (other schools go more slowly and spread it out over two semesters). OP: are grad students allowed to take a class like Math112 at Harvard? If so, I would strongly recommend taking this.

I would take real analysis, since you don't have it on your transcript. Judging from these course descriptions, Probability I is just the first semester of the year-long sequence of Mathematical (Theoretical) Statistics I & II, so there does not seem to be any point in taking it separately from the typical Masters-level mathematical statistics sequence. For Probability II at your institution, the instructor probably won't allow you to take it if you haven't taken a basic analysis course. And you can take this in your PhD program anyway (at most stat and biostat programs, this would be the required PhD-level course in Probability). Many PhD programs only require one semester of measure-theoretic probability theory (including reputable programs such as CMU and Duke), with an optional second semester of advanced probability theory for the students who plan to specialize more on probability theory than on statistics. I did my dissertation on theoretical stats, and I only needed to know the very basics of measure theory and probability theory for my research.

No. A certificate, a Masters in Data Science, or a Masters in "Applied Statistics" (they have those now) would not be sufficient to get admission to a Statistics PhD program. However, obtaining a Masters degree in Mathematics (pure or applied) or Statistics, where you can overcome some deficiencies in preparation, would certainly qualify you to get into some Statistics PhD program. Maybe not a top-tier one like Stanford or Berkeley, where they seem to want those with an extremely high level of mathematical ability/background, but you should still be able to get into one. My current program is solid, but not top-tier, and we have had PhD graduates who did not major in math as undergrad but who obtained mathematics Masters degrees, then enrolled in our PhD program, and went on to have great careers (one such alumnus from 2004 majored in Journalism as an undergrad and is now a Professor at University of South Carolina; another one just graduated just last year and is now working as a Senior Data Scientist at a big company in NYC). If you truly want to get a Statistics PhD, someone with your background would need to first get a Masters in math or stat.

Assuming that you will still be funded for the next semester, I would just complete the second MS (since it's not in the exact same field as your previous Masters) and apply for jobs while you're wrapping things up. That way, you can put the MS on your resume and it doesn't look like you have a 3-year employment gap. Additionally, I presume that you worked as a TA (or RA?) during your PhD, so you can reframe it as work experience on your resume (either as something like "Graduate Student Instructor" or "Research Assistant," whichever is applicable). You don't have to fall for the "sunk cost" fallacy. There's nothing wrong with leaving a PhD program -- a lot of people realize that the research life is not for them and leave as ABD, and they go on to have great, fulfilling careers afterwards. In fact, some people who *do* finish the PhD go on to become lecturers or professors at community colleges, because they determined that they love teaching but absolutely hate research! Your mileage may vary. If you have difficulty letting it go, then perhaps speak with a counselor who can help you come to terms with it.

Since you studied engineering at an Ivy League school, I imagine that you would have a pretty good shot at top programs if you perform well in your Masters program. For Statistics and Biostatistics, you certainly need to take real analysis -- I would recommend two semesters of it. In general, it does not seem like the specific choice of Statistics electives is that crucial, but I would probably swap out Data Science I and Data Science II on your planned courses with courses that are a bit more "mathematical" (like Multivariate Analysis, Stochastic Processes, Numerical Optimization, Mathematical Programming, Numerical Analysis, etc.). These courses would be much more relevant to Operations Research and Statistics/Biostatistics.

I think you are a strong candidate for Masters programs, but I'm not sure about PhD programs (in Statistics anyway, I'm not as familiar with Biostatistics)... since you're not a domestic student, the bar will be a lot higher for you and preference will be given to international applicants with a strong math background. If you want to attend a higher ranked PhD program in stat/biostat, you may want to apply primarily to Masters programs but also try your luck with some PhD programs too. At some top schools in Biostatistics, it seems like there is a pipeline for top-performing Masters students to continue on to the PhD. Just something to consider.

You would need to apply separately to Masters programs. Given your current profile, I think most of the schools on your list are out of reach (for PhD), so I would reduce the list of PhD applications substantially and focus primarily on Masters applications. Assuming you perform well in a Masters program, I think you would have a shot at maybe a school at the level of Ohio State or UF (but maybe still not at the tier of UMN). I would also consider biostatistics programs if you are interested in spatial statistics.

It is going to be tough for you since your GPA is a bit on the lower side and you did not attend a prestigious school where a slightly lower GPA could be forgiven somewhat (e.g. UChicago, MIT, Caltech). Even a place like University of Georgia is probably a reach. Schools at the tier of George Mason and below seem more reasonable but not guaranteed either. If you are determined to get a PhD in statistics, I think you will need to get a Masters first and take more upper division/graduate-level math classes too to demonstrate that you can handle the graduate coursework (which will be very theoretical and mathematical even if your research ends up being on the more applied side, e.g. with spatial statistics).

I think you can probably get into most Masters programs, as the bar tends to be lower for Masters admissions and the you have the additional plus that you attended UChicago. I also attended a "prestigious" school for undergrad (an Ivy) with a reputation for grade deflation and had little difficulty getting accepted into Masters. You can probably get into the Statistics MS program at University of Chicago. Would that interest you?

I would add to this comment that it is becoming increasingly the norm that PhD graduates in Statistics must complete a postdoc in order to land a tenure-track professorship job (some exceptions might be if you go to a top 20 program *and* have a strong publication record upon graduation). And if you do complete a good postdoc, that outweighs your PhD institution byfar. There is one alum from my school who did a postdoc at CMU and is now an Assistant Professor at Duke. So going to 30-50 school is not as likely to yield a TT job right away, but your chances improve dramatically if you do a good postdoc (and obviously, you're productive during the postdoc years). My department has just hired two new faculty members who got their PhDs from UCSC and University of Cincinatti, but their postdocs were at Duke University. Hiring committees look at candidates' most recent position and publication record when they decide whom to shortlist. So I would agree that getting a TT job immediately upon graduation from a PhD program outside the top 20 range is more difficult, but this can be compensated with a prestigious postdoc. So if you want to go to the academic route but attend a somewhat less "prestigious" school for your PhD, work with the best advisor you can and try to land the most prestigious postdoc you can.