As a Canadian who has a very similar profile to you and just went through application season, I'll try to throw in my 2 cents. I think the two above posts about international students requiring publications and PhD courses is more relevant for students from China/India (let's be honest, that's 90% of international applicants). As Canadians we are looked upon a bit more favourably by the US, and UofT is the best school in Canada (small bias as I'm doing my PhD there), so your profile will definitely be noticed. I do agree you're weak for pure math courses, but all I had completed when I applied was a semester of real analysis -- although I was enrolled in the second real analysis and measure theory. You don't have many upper year courses listed up there, but engineering is notoriously difficult at UofT so I'll assume that you've taken a rigorous course load. If you can, enrol in real analysis and the third year mathematical stats course at UofT (where you learn the derivations behind hypothesis testing and inference) so that the admission committee will see that you're serious about mathematically mature courses. It's a little hard to tell from your experience how much research you've actually done, but if your referees can speak to your research potential that will be critical for your application. I think having my USRA supervisor write about my research potential is what helped me the most, so you want profs like this more than you want profs who can only say you got 100 in their class.
If you want to do a master's, stay here in Canada where you'll be fully funded. I think you're guaranteed admission pretty much everywhere here since that was my experience and I don't see what would have made me stand out above you. For US schools, clearly CMU seems more open to accepting Canadian students, but I think you're also a good candidate for Washington. Any school that isn't top 10 I think you have a shot at getting in, but for Harvard/Stanford/Chicago I think you'll need more math courses. Your math GRE mark could also serve to really boost this part of your application if you get a very high score. If you know what area you want to do research in that will also help to identify where to apply.
There are a few other current PhD students who frequent this forum. I've visited it on and off over the years, but I have not seen many posts from current PhD students about their experiences. I thought this may be of interest to potential applicants, so I decided to write about what I have learned (I am about to graduate, finishing my final defense and thesis in May). I am happy to report that my PhD experience was largely positive.
1) A PhD program is fundamentally a research degree, and research is nothing like taking classes. I think some Stat/Biostatistics programs do a great job of involving students in research early on through rotations with different professors or through reading courses to familiarize students with statistical literature. But there are a lot of programs where students do not start research until the end of their second year. And I have seen many PhD students who were very, very bright (acing all their classes, 4.0 GPA, etc.) but who really struggled with transitioning from being a student to becoming a researcher.
I definitely think you should work hard in your classes so you can pass your written qualifying exams and so you can developed a solid foundational understanding, but once you get to the research stage of the program, you really do have to teach yourself a whole new area. Moreover, research is about discovering something new and pushing the boundary of your field. There is just no way of knowing if some "open problems" can be solved or not! It's not like solving a problem on a homework set where there is generally one correct solution/approach. If you do a theoretical topic for your dissertation, you need to prove new theorems that have never been established before, not just "show” something that already has a known solution. And even if you start working on a problem, you may get stuck for long periods of time (or need to cut your losses and give up), or you may end up somewhere completely different from where you started. Unlike problem sets and exams, there are no concrete solutions. For example, for the first paper that I wrote, I was stuck on a proof for my main theorem for three whole months. Nothing I tried seemed to work! But my PhD advisor pushed me to keep trying, and eventually I found the technique that worked. Phew!
2) A lot of the learning in grad school happens outside the classroom, and you need to ask questions. This comes from talking with your peers, meeting with your advisor, attending departmental seminars, and reading papers. Here is the thing: when most people start research, they do not yet have the skills to really excel at it. A small number of people are able to excel right from the get-go, but for most people, it takes a bit of adjustment, and that's okay! It is important to reach out for help if you need it. If I didn't understand an author's proof or a new concept that I had never encountered before, I would ask my advisor to help me. I didn't have much experience with high-performance computing or running simulations on multiprocessing systems, so I asked my more experienced classmates to help show me how to navigate it.
3) Everybody thinks about quitting at some point. This is perfectly normal. A PhD can be a very demoralizing, frustrating experience. Plus, things can happen in your personal life that can derail you. It's just part of life. When I felt like quitting, I just took some time off... maybe 2-4 days of not doing any work to recuperate and assess why I was putting myself through the PhD. After some time off (not too much time off), I could reason to myself why I wanted to get a PhD, and I got right back to work. So if this happens to you, accept your feelings, take a breather, and then really question your own motivations for pursuing a PhD. If you can answer this question to yourself, "Why do I want a PhD? Am I willing to 'tough' it out when I'm feeling frustrated?", then you will be able to pick up right where you left off.
4) Just about EVERYBODY gets their papers rejected, even Distinguished Professors and Nobel Prize winners. My PhD advisor has co-authored over 250 papers and is quite smart, and he still has papers rejected. Professors at all levels get their papers rejected, some multiple times before they are finally published. It’s part of the process.
It also happened to me for the first paper I ever submitted. Rejection always stings, but I say if it happens, take a deep breath and cool off a bit. Once you’ve acknowledged the disappointment and cooled off, read the referee reports and comments from the Associate Editor very carefully. Peer review is inherently a subjective process, but for the most part, paper referees take their jobs very seriously, and there will be valid concerns and comments for improving your manuscript (even if some might not be the most diplomatic when letting you know the faults they find with it!). It may be that the journal you submitted to just might not be the most appropriate venue for your work. Or there may be more substantive changes that are needed to make your manuscript more acceptable for publication.
After my first paper was rejected, I spent a lot of time with my advisor revising it. We eventually re-worked the whole paper (e.g. cutting down the length of the literature review to the most essential points), we proved a new lemma and a new theorem that showed our new estimator’s improvement over previous estimators, and we performed several new simulation studies that showed quite interesting results. We just resubmitted this paper, making appropriate changes suggested by the peer reviewers who had rejected the manuscript, and I have to say my paper was way better than before. The paper was better off in the long-run.
5) The choice of PhD advisor is critical. It's very important that your PhD advisor is someone whom you can have a great working relationship with, whose research is interesting to you personally, and who is actively publishing in respectable journals. I think the last two are more important than anything else, especially for academic jobs. You basically need to have quality papers and excellent recommendation letters if you want to get a good postdoc or faculty position. Some PhD students are hesitant to work with Assistant Professors and are "star-struck" but there's really no point working with a world-renowned professor if their mentorship style and their research does not align with your personal working style/interests. Plus, an Assistant Professor who is actively publishing their work in top journals can still help you develop your career.
Some people need a bit more guidance and an advisor who gently “pushes” them, while others can operate fairly independently and do not need to meet their advisor very frequently. The working style of you and your advisor should mesh well if you hope to be productive.
6) The fields of statistics and biostatistics change very rapidly, so it's more important that you do research that "comes from the heart" than try to keep up with a "hot area." I would not recommend researching a topic that is so archaic and obscure that only a tiny number of people in the world are still working on it. But I also think that you should prioritize your personal interests above what's currently "hot." It can be very difficult to predict what will be "hot" years from now. For example, Dirichlet processes were not very popular when the concept was first introduced, but decades later, Bayesian nonparametrics have exploded in the field of machine learning. It used to be that SVMs were very popular and neural networks lost some of their popularity, but currently, it is the opposite. There is an explosion of interest in neural networks/deep learning and not as much in SVM. The fields of statistics and biostatistics are constantly evolving and changing, so trying to "time" your thesis to a "hot area" can be tricky.
But most importantly, a PhD is a very time-consuming commitment (at least 2 years of research). So you do not want to be miserable the whole time you are doing it. So make sure to pick a thesis topic that you find interesting. You probably won’t be able to do that yourself at first, but to that end, your advisor will help you hone in on some interesting open problems to work on. Do not do a topic that you have no personal interest in! Sure, some people might be more impressed if you do (what they perceive to be) a more "difficult" topic, but at the end of the day, you're the one who has to live with yourself and your career choices. And if your heart just isn't into it, it will make finishing the PhD much more excruciating.
7) Do not assume that your PhD thesis topic is the only thing you will work on for the rest of your career. To tie in with my previous point, you can always change gears and switch to a “hot” research area after you are done with your PhD. Finishing the PhD is the start of your career and certainly not where you want to peak. A PhD dissertation is usually on a specific, narrow topic or set of topics. Some people are lucky and can milk their research area for the rest of their career, but many people aren't that lucky.
Even if you want to go into industry, an employer of PhD graduates is going to expect that you can teach yourself new things (new software, new models, etc.) on the fly, even if you've never seen/used these things before. In fact, it is this creativity and ability to learn new things quickly that makes hiring a PhD graduate more appealing than hiring someone with juts a Masters. Likewise in academia, professors are teaching themselves new things and moving into new areas all the time. My own PhD advisor began his career doing frequentist nonparametric statistics, but now he has research in a variety of areas of Bayesian statistics. The postdocs I am currently considering are in entirely new areas that I haven't learned before. By the end of the PhD, you should ideally have enough maturity and initiative to teach yourself different areas of statistics.
Thanks statscan, I agree with you on both points. My goal to eventually pursue a PhD is to enhance my own understanding of the field; the job I get afterwards would only be a product of immersing myself in statistics.
Rejected from Columbia. Went from a strong start to a disappointing finish, maybe being an international was more of a detriment than I expected. Also seems like not taking the subject GRE was a mistake. Oh well, ultimately happy with my outcome, and glad I never have to go through this process again lol.
Rejected from Columbia. Went from a strong start to a disappointing finish, maybe being an international was more of a detriment than I expected. Also seems like not taking the subject GRE was a mistake. Oh well, ultimately happy with my outcome, and glad I never have to go through this process again lol.
Rejected from Columbia. Went from a strong start to a disappointing finish, maybe being an international was more of a detriment than I expected. Also seems like not taking the subject GRE was a mistake. Oh well, ultimately happy with my outcome, and glad I never have to go through this process again lol.
I've got an acceptance to the direct entry PhD at Toronto as well as an unofficial offer (from a supervisor) for McGill's MSc. Not sure if Toronto waits to do the MSc until after they've sent out the PhD letters?
Not much to say, really. You're a strong candidate, so you should apply to all the good places in the places you'd like to live. Stanford is a tough nut to crack for Canadians, but seems like a logical addition to your list (though you might have to take the Math GRE, which is a pain).
@insert_name_here I can't speak for OP since I don't know what school he attends but at my school we have less grade inflation than at US schools so our GPA has to reflect that. We actually get grades in terms of percentages, and then those are converted into GPA, roughly as follows: 50-60% is a D, 60-70% is a C, 70-80% is a B, 80-90% is an A, 90-100% is an A+. The average grade for almost all of our classes is between 60% and 65% (so a C). My marks (virtually all A+, with an actual average of 96.5%) put me in the top 2-3 of my class for the Statistics and Actuarial Science department (~200 undergrads in my year). My supervisor (who knows the top marks) says I'm likely going to win the award handed out at graduation for highest graduating average, so I might actually be the top student. We definitely don't just hand out marks here, in fact our averages are lower than what most US averages are from what I understand.
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