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Stats PhD 2019 Chances

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Hi everyone! I'm trying to get a sense for my PhD or masters prospects for statistics, and would really appreciate any help!

Undergrad Institution: University of Toronto
Major(s): Industrial Engineering, focusing on Operations Research (Bachelor of Engineering)
GPA: 4.0/4.0 Cumulative GPA (94% average)

Relevant Courses:

Calc I (for engineers): 99

Calc 2 (for engineers): 100

Calc 3 (for engineers): 98

Applied Linear Algebra: 96

Probability: 100

Modelling with Differential Equations: 100

Statistics and Design of Experiments: 96

Data Mining (taken in Statistics Department): 97

Time Series Analysis (taken in statistics department): 93

Type of Student: International (Canada) Male
167 Quantitative
163 Verbal
4.0 Analytical
Taking the GRE Math in September
Programs Applying: PhD in Statistics (or masters)
Research Experience: Doing an undergraduate thesis in my last year, focusing on applying machine learning to the reliability/manufacturing engineering.
Letters of Recommendation: Likely one from thesis advisor (operations research professor), one letter from my 8 month internship working on reinforcement learning, and likely one from another professor in my faculty (there are two professors where I got 100 in two of their classes). I also have another professor that would write me a terrific recommendation letter (went truly above and beyond in an applied course), but she is part of the business faculty.
Computing Skills: R, Python, SQL, Java, C
Work Experience: Spent two summers working as a software developer, and 9 months working at large bank on applying reinforcement learning to capital markets (research intensive).
-Worried about my math background (specifically no real analysis course - although I plan on taking one in my final year), especially coming from a non-maths undergraduate background
What schools would be attainable with my background? The goal was originally to apply for top tier programs (Stanford, CM, Chicago) - but I probably need a bit of a reality check. Anything I can do to bolster my chances?
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Taking more analysis and optimization courses definitely helps. I have a chinese friend who got into stanford this year. He basically took all possible graduate analysis courses and convex optimization class in his institution. Bars for international students nowadays are significantly higher than the past. Publications are often seen and majority of them already took phd level courses. I have seen people with similar stats with you getting rejected from all top 15 including biostat. You should definitely expand your list to at least top 25, if your sole purpose is attending a PhD program. I would strongly recommend including larger programs like NCSU and Iowa. Things are damn hard nowadays for international applicants.

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You have a very strong profile for just about any Masters program, but your math background is a bit sparser than other applicants for PhD programs (in Statistics). Taking an advanced proof-based linear algebra class and a real analysis class and having good grades in these on your transcript should boost your application. As for publications, a lot of international applicants will have one (most likely not in in a venue like JASA, Annals, JRSS, etc., but sometimes in a business or an econometrics journal or a less prestigious stat journal), but I also don't think it is required to get admission to a reputable school. Admissions are very tough though, so I would apply widely.

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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. 


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If you take real analysis first semester next year, and get an A so it's on your transcript, I agree with statscan9.  Top 10 would need more math though to have a decent shot. Admissions for Canadians is not that much worse than for American's, certainly not like the competition for students from India and China. 

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