StatsG0d

I agree with @bayessays. Most students will basically have taken up to Real Analysis and not much extra. Some students even get admitted without RA, although this is becoming more rare. I do think that the more you have, the stronger your application will be. So if you're fighting for the top programs, it definitely won't hurt to take more math (provided you earn good grades in those classes).

I think it matters more that you have letters that attest to your mathematics ability than your statistics ability.

Your math background is extremely broad, and you've received a bunch of high grades in graduate level math courses. That said, it's hard to know how adcoms will view you because of your undergrad GPA and getting low grades in calculus / linear algebra, which are the two most important prerequisite courses in statistics / biostatistics. You will have to address these discrepancies in your SOP. Given your math background, I recommend that you take the math subject GRE. I think you could do quite well on it, and if you do, no one is going to care about your undergrad grades as a lot of material on the math subject GRE is calculus / linear algebra.

I don't think biostats is more competitive than stats. Probably more the contrary. Very few students have any relevant research experience coming in. To me, it sounds like your research experience does relate to biostats, as high dimensional data is common (e.g., genomics) and so is shrinkage (e.g., Bayesian analysis). To formulate your interests, I recommend you read some papers or just google some fields that are popular in biostatistics and relate to the branch of statistics you are interested in, e.g. Computation - genomics Machine learning - precision medicine Spatial/temporal - Image analysis (e.g., diagnosing cancers based off of an MRI) Bayesian - design/analysis of clinical trials Virtually every subfield of statistics has applications in biostatistics.

If you are interested in applied statistics, I don't think UPenn would be a very good fit. The other schools on your list seem reasonable (maybe not Iowa state though). Have you considered biostatistics? I think you would have a very strong profile.

Although your GPA is quite low, you have several published manuscripts and your math background is very deep. I think you have a shot at the schools in the 5-10 range. I would apply to all of those (replacing your least 5 favorite schools in the above), and see what happens. Most of the programs you listed are very unknown. It's not clear they would want someone who appears equipped to be a methodologist, as many of these programs are applied. If applications are your interest, I would clearly state this on your SOP, because based on your math background I would think you would want to be a methodologist.

I agree if the OP meant stats departments then they should apply to those. I assumed they meant biostats

I apologize if I confused you. I didn't mean the "applied real analysis" course specific--just a general course in what most institutions call real analysis. Advanced Calculus is the way to go. Perhaps that's the confusion surrounding your advisor's saying no one takes it.

The problem with NYU and Northwestern is that both programs are highly selective relative their ranking. This is typically because some international students care more about university prestige rather than departmental prestige. The other schools don't seem bad. If being in a somewhat large metro area is important to you, you can apply to some of the larger programs in those areas such as NCSU (downtown Raleigh), OSU (Columbus, OH), Minnesota (Minneapolis, but cold). Some of the larger state schools in smaller areas tend to have really sophisticated bus systems that can get you around relatively efficiently without a car (e.g., Florida State, Iowa State, South Carolina, etc.) You can browse through each school's / community's transit page and see where the buses go and how convenient it would be to e.g. live somewhere within walking distance to a grocery store and being able to take a bus to campus.

I think you're selling yourself really short. First, I wouldn't bother applying to UCSD, TAMU, Rutgers, or Rice. NCSU doesn't have a PhD in biostatistics, although they do have a Biostatistics concentration in their Statistics department. Also, not sure if UW refers to Wisconsin or Washington. You're competitive for any of the biostats programs in the top-5. In fact, I would be shocked if you didn't at least get into one of UNC or Michigan. I would say apply to all the top-7 biostats programs and maybe those Canadian schools if you're interested. I'd maybe add McGill if you're interested in precision medicine. I'd also add Berkeley if you're interested in causal inference. It sort of depends. If you've taken all the qualifying exam courses, the department *might* let you take the qualifying exam the summer you arrive. Otherwise, they may force you to retake their versions of the courses and then take the qualifying exam at the end of the first year. It usually depends on both the department and the specific case. If the qualifying exam is taken in the 2nd year (e.g., how it is at UNC), they'll let you skip the first year curriculum, but you'll have to take the 2nd year curriculum and take the qualifying exam the summer after your first year.

It's really hard to say. Typically, a lot of non-US universities have sort of a pipeline with various US-based PhD programs. If yours doesn't have that, it's honestly a crapshoot. Your best bet is to apply to schools that tend to admit a lot of international students (e.g., University of Florida comes to mind). There are probably many others, but that's the one I know for sure tends to admit many international students. Browse this forum--I'm positive others have mentioned other programs.

You should check out mathematicsgre.com, as this forum is really biased more towards statistics than math.

It's possible (and highly likely) that the other students had already taken the course (e.g., in undergrad). You definitely need to take real analysis for stats. You *might* be able to get away without taking it if you're doing biostats (although, this is becoming less common at the top 5-7 programs, as the field is becoming more competitive). Even if you managed to get into a program without taking analysis, you would have wished that you'd taken it. Even in Casella-Berger level Math Stats, real analysis is very useful for making mathematically rigorous arguments / proofs. I feel like you (or anyone without real analysis) would struggle in a pure stats program without it. Any/all of those courses will be useful when you reach the dissertation stage, but the reality is adcoms don't really care much about how many statistics courses are taken (unless they're mathematically rigorous courses e.g., linear models, probability theory, (martingale-based) survival analysis, etc.). If I'm on an adcom and I see that you've taken these stats courses, I'll think "OK, it's nice that they clearly have shown an interest in statistics, but how prepared are they to be successful in the program?" I'd look at the GRE and see a lower score relative to other applicants, and then think "well, perhaps this student had a lower GRE score, but has demonstrated mathematical maturity through courses." Then, when I see the lack of a single proof-based course on the profile, I would almost certainly reject the applicant. I think it's important for you to reflect deeply and see if you know what you're getting yourself into. If you are trying to avoid taking real analysis because you dislike theory, then I can assure you that you will not like doing a stats PhD, and you will burn out really quickly. The courses / qualifying exam is difficult even for those that have taken real analysis, and I truthfully can't imagine an individual doing well without it, especially relative to peers. If you are more interested in the application of statistics, there are other fields you can consider that utilize advanced statistical methods (e.g., epidemiology, psychology, quantitative methods in the social sciences) without the need to dive into the theory. The purpose of a stats PhD is to make you equipped to develop your own methods.

This is exactly what I was trying to say regarding Kosorok vs. Hudgens and causal inference / precision medicine above, but is a more elegant and general answer. Couldn't agree more. I totally agree with you, but I figured I'd let the OP decide / figure out which programs are suitable.

It's a fair question. To me, most of causal inference is concerned with identifying a population average treatment effect (typically not adjusted for covariates), while precision medicine is mostly concerned with which treatment for which individual at what time. Most of traditional causal inference utilizes classical statistical techniques (e.g., regression, GLM, etc.), albeit with some adjustments to account for confounding. In causal inference, it's really important to prove things such as consistency and asymptotic normality. In precision medicine, a lot of the methods are more machine learning focused. They might prove consistency, but asymptotic normality is a bit rarer. I guess I just feel precision medicine, while a specific case of causal inference, is a lot different than other fields with specific cases.

If you have the prerequisites, epi and econometrics are good disciplines for causal inference research as well.

Kosorok really works more in precision medicine, which is kind of a special case of causal inference. Hudgens works in causal inference with a focus on interference (i.e., when one individual receiving treatment impacts the probability that another individual receives treatment). A lot of faculty in the Epi department at UNC works in causal inference theory (e.g., Stephen Cole).

I did an internship in front office quantitative finance and ultimately I realized the position was really a glorified software programmer. Sure, they used statistics (although I was once told to “do data science”), but the job was really about developing software to create nice plots. At the end of the day, whatever you do as a data scientist / quant has to be explained to a larger audience who will know very little if anything about statistics / ML All this to say: you can’t judge a job by the title / job description. And I’ll echo the others and say the vast minority of my time is actually spent coming up with new methods. Most of it is running simulations or programming or finding the perfect way to texify a data frame.

If you're doing research, I think it's crucial. In general, you want to prove some asymptotic properties of your method, whether it be it's consistent or asymptotically normal what have you. The NYU data science PhD program requires a sequence in probability and statistics. One component of the course is convergence, so these topics will definitely come up again. Stuff like this is, in my opinion, somewhat insulting. I realize that you are not intending it to be so, but note that many of us (but not me) on here have devoted our entire careers to asymptotics and they are important. Showing your estimator is consistent and/or asymptotically normal is really important. You mentioned earlier causal inference, well this is basically what causal inference people do--here's a new estimator that's unbiased / consistent and asymptotically normal. It's fine if you feel like biostatistics / statistics isn't for you, but you should not come on a statistics forum and basically put down everything and say it's "outdated" or "boring".

Power and sample size can become quite sophisticated (see, e.g., the literature on probability of success / assurance / Bayesian power). I'm surprised to hear about the not doing imputation though. I imagine that would raise the eyebrows of regulators if there are a lot of missing data. I don't know the size of the place you're at, but there are many people working in pharma that are extending clinical and regulatory science. Sounds like you might be at a smaller place or a place that doesn't encourage such work? Forgive me if I implied this. My point was that uncertainty quantification is what sets apart statistics from ML. ML, at its heart, is mostly about optimization (I know there are many probabilistic algorithms etc., but the vast majority of algorithms are deterministic and focused on separation, etc.). If you're interested, there's a great presentation by Lisa Lavange (former head of biostats at the FDA, current chair of Biostats at UNC) talking about some initiatives being undergone at the FDA. This is verifiably false. Here are several job postings from pharma companies / CROs dealing with the analysis of RWE AstraZeneca JnJ Novartis Cytel Bayer Boehringer UCB Harnham Moderna

I'm not sure this is fully true, as tech companies are really more focused on machine learning / AI than statistics IMO. I guess it depends on what you mean by "real" statistics. To me, real statistics is about quantification of uncertainty, and that is the primary difference between (bio/)statisticians and ML folk. The regulatory constraint is actually more of a methodological interest than a limitation--how can we maximize power / the likelihood of approval subject to the analysis constraints that the FDA sets. Topics such as type I error / multiplicity become increasingly important in drug approval. Moreover, the FDA has recently begun investigating the use of real world evidence (RWE) and Bayesian methods for drug approval. I agree that the regulatory constraint does limit ones creativity compared to, say, a tech company that can do whatever it wants. However, strongly disagree that tech companies are more statistically rigorous than pharmaceutical companies--I think the contrary is true. I foresee that the FDA will allow more creativity in its analysis, particularly in observational data settings for the long-term safety / efficacy of medical products. To me, it seems that you do not have a good idea of what it means to be a statistician (forgive me, I am not trying to criticize you here). Being rigorous mathematically and statistically and actually thinking about the data / problems that could arise from it is what fundamentally sets statisticians apart from our data science counterparts. We are very concerned about assumptions in the data, what could possibly go wrong, how missing data could influence inference on the treatment effect, etc. I agree with you that if all you'd like to do is conduct data analysis, perhaps biostatistics is not a good fit for you. Conversely, getting a PhD would likely increase the flexibility you have with your work. Finally, while tech companies have, thus far, been unregulated, it's not clear that the future will be the same as the present. As more people are becoming concerned with data privacy and security, I think it becomes more likely that tech companies will be regulated, which would likely put them in a similar situation as drug / finance companies.

I don't agree with this at all. Wake Forest is a very reputable school and there's a list of institutions that their Master's graduates end up attending, many of which are very prestigious. Not sure if you're trying to actually take a knock at Wake Forest in particular or if you were just oblivious to this fact. I think the OP has a great chance at top-20 programs and a small but nonzero chance at a top-10 stats. I could see them getting into any/all of the top-5 biostats programs. Their mathematics knowledge is extremely deep--far deeper than the vast majority of domestic students. They have a letter writer with connects at the institutions in which they are applying. Got a perfect GRE Q and writing score. This is a really strong profile IMO. The biggest problem is going to be that it seems the OP has quite specific research interests. I think it will be difficult to find a good program that aligns with these interests. OP: I recommend you apply broadly (a couple in the top-10, most in the 11-30 range, some in the 30+ range to be "safe"). I do NOT advocate for speaking about your specific research interests in your statement of purpose, because I think if it's not a departmental interest they will be likely to reject you. Simply say you're interested in high dimensional statistics or something.

I think if you explain in your statement of purpose the reasoning behind the grade it's definitely not a deal breaker. I think adcoms know/understand that it's difficult to learn in a virtual environment.

Yep mostly this (although I do feel like this has been changing in recent years). The top-4 programs are known to be pretty mathematically rigorous. Perhaps not as much as stats departments, but much more than the rest of the bunch. I think there are some schools that will automatically consider you for MS admissions if you don't make the PhD. You could target those schools. Also, a lot of the programs have a process for internal PhD applications (e.g., I know UNC does). So you could also apply for an MS at a program where you'd like to do a PhD and see how that goes. I feel like that's a better option than applying to MS and then applying to PhD because you'll spend a lot of money in a 2 year MS program.

You'll probably get into all of those MS programs. In fact, I think you're competitive for any MS program in stats in the country, so take your pick. You might be able to get into some PhD programs ranked 30-50 directly if you're interested in that. This is particularly true if your school is known for some type of grade deflation that would bring your GPA into some light. While the GPA is somewhat low, you did go to a very good undergraduate institution and have a pretty broad math background. I'd be shocked if you didn't get into at least one stats PhD program 30-50 or biostats PhD program ranked 6 and below.