Phd in Statistics Suggestions

[frequentist]

Undergrad: Big State School ranked around 150

Major: Mathematics, with Minor in Computer Science

GPA: 4.0 (Two more semesters to go)

Student Type: International Male (South Asian)

 Courses:  Calculus Series, Into Linear Algebra, Differential Equations, Proofs and Logic, Discrete Mathematics, Undergraduate Advanced Calculus Series, Intro to Programming, Object Oriented Programming, Data Structures, Data Science in Python, Data Visualization in R, Database System, Elementary Number Theory, Group Theory, Mathematical Statistics I, Mathematical Statistics II, Analytic Number Theory, Complex Analysis, Probabilistic Number Theory. Currently taking Graduate Real Analysis I, Probability Theory I, Proof based linear algebra. Will take Real Analysis II, Probability Theory II, Topology next semester

 

GRE General: Taking third week of October. Hoping to 165+ in quantitative

Math GRE: Not taking

Research: Proved a small result in analytic number theory with my advisor. Participated in summer research program at The Fields Institute where I worked in Arithmetic statistics. I worked primarily in simulation and generating data where I wrote parallel programs in C++ using OpenMP and MPI and used supercomputers to perform simulation. Got some interesting results, currently writing a paper to submit. I am also currently working in probabilistic number theory with my another advisor and we proved an interesting result, currently brushing up the work. 

I have a decent background in computation and pure mathematics, which stat grad school seem to value a lot. But I do not have a strong background in the thing that matters most, statistics. 

Letters of Recommendation:  I think I will get strong letters from all three people I have worked with. 

Programs Applying to: Statistics PhD

My questions are:

1. I initially thought I would do number theory in grad school, but as I started working in probabilistic number theory and arithmetic statistics, I found out that I loved working in problems in statistics and applied probability more and I also realized how powerful statistics is (for example we were able to generate data and verify a conjecture with statistical analysis that seemed incredibly difficult to approach with traditional mathematical tools).   Should I just be honest in my statement in purpose and say I how I got interested in statistics but do not have any narrow interest figured out but will take classes in grad school and see for myself what I enjoy most? Or should I write some pretentious crap about how I am interested in some fancy sounding field and want to work with X,Y,Z professor? But I guess being honest I might not be able to convince the admission committee that I am a good fit for their department.

2. Although I have a good research background, I do not have any publication till now. Opportunities just came by and I went on doing multiple projects than sitting down to write up the results and finalize the work. Depending upon how hard I can work, we might be able to upload 3 papers in arxiv while submitting our application but I wont have a manuscript of my strongest result. Will I be able to make a case for me in good school if I do not have any publication? But both I and my advisors will be able to give brief but precise account of exact works I have done and results I have proved. 

3. Since I come from a department which has almost never sent a student to top schools, do I stand a chance at top programs? I think I have worked incredibly had during my undergrad but there is always a reputation of school that might potentially hurt me. 

4. All three people I have worked with are number theorists, and if I ask for fourth the person that will be able to write the best letter for me is my probability theory professor. I took two statistics class with the same professor, got A in both, but do not have great relationship with the professor. Does not having letter of recommendation from a statistics professor send a bad message?

 

Sorry for the long ramble!

[StatsG0d]

1. There are many students who do not have a big stats / probability background that are accepted to PhD programs. Usually the problem would be the opposite--people apply majoring in statistics or another quantitative discipline but do not possess the required math background. Your background is fine, and I think the motivation you mentioned already sounds good for the SOP.

2. Few applicants have meaningful research experience. I think simply mentioning that they are on arxiv will be more than enough.

3. You definitely have a good shot, and it's better to come form a lower tier US university than an unknown international one (even though the latter might be more rigorous). It's a lot tougher as an international student, but I think your GPA and math background are enough to get accepted to some top-30 programs. There are a lot of schools that tend to recruit many international students (UF, FSU come to mind). I'd be surprised if you didn't get into at least one of those.

4. I don't think it sends a bad message. What matters is that your letter writers can attest to your ability to do math. It's great if it comes from a stats professor, but I would rather have 3 letter from people whom you know are going to write something positive than 2 positive and 1 neutral.