Stat/OR PhD profile evaluation and advice

[baxterbotox]

General questions: who of the listed options should I ask for letters? what kinds of programs are realistic for me? not sure how much it matters but (I think) I am interested in decision models, reinforcement learning, and stochastic optimization.

Undergrad Institution: Top public, good for stats (e.g. UNC, Michigan, UCLA, UW)
Major(s): Statistics and math
Minor(s): None
GPA: 3.95
Type of Student: domestic male

GRE General Test: lol no
GRE Subject Test in Mathematics: lol no
 
Programs Applying: PhD Statistics, PhD Operations Research

Research Experience: 

• Funded research at home institution (1.5 years): worked on a project in low-rank matrix reconstruction
• REU after 3rd year: worked on a project in reinforcement learning
• REU after 2nd year: worked on a project in graph optimization algorithms

Awards/Honors/Recognitions: nothing important; dean's list every semester and 2 nonzero Putnam scores (lol)

Pertinent Activities or Jobs: TA for undergrad real analysis (2x)

Letters of Recommendation (I have four good options so please advise me on which three to ask; leaning towards 2,3,4): 

1. 1st REU mentor (CS assoc. prof): okay, I mostly worked independently with little supervision and made some progress but not too much in way of a nontrivial result.
2. 2nd REU mentor (CS full prof): fairly strong, I had a lot more mathematical background, rigorous understanding of the topics, and interest in the project so I was able to make a lot more progress.
3. Home institution research mentor (stat asst. prof): fairly strong, I was pretty useless at first as I wasn't putting enough time in but shaped up and I feel my mentor is reasonably satisfied with the progress I have made.
4. Real analysis prof (math full prof): fairly strong, was one of the best students in his course and TA'd for him twice for the same course; he also wrote a letter for me both times I applied for REUs.

Math/Statistics Courses (all As unless otherwise indicated):
    Undergrad: Calculus 1-3, ODEs, Discrete Math (Intro to Proofs), Real Analysis I-II, Linear Algebra I-II, Numerical Linear Algebra, Combinatorics, Optimization I-II (A- in II), Abstract Algebra (B), Probability I-II, Theoretical Statistics, Reinforcement Learning, Numerical Analysis (current)

    Grad: Measure Theory, Measure Theoretic Probability, Stochastic Processes I-II (A- in I), Simulation, Reinforcement Learning (currently taking), Optimization I-II (currently taking I, will take II in spring), Theoretical Statistics I-II (currently taking I, will take II in spring)

Applying to Where: Will not be too specific but applying to some of the most competitive programs (pls at least one of stanford stats, MIT ORC, princeton ORFE let me in). Some lower ranked ones too, think the lowest ranked on my list right now are rice and UT. would appreciate some advice on what range of programs is realistic for me and where I should cut off and not bother applying to anything lower.

Any Miscellaneous Points that Might Help: yesterday during my office hours as real analysis TA I told a student that -x must be nonnegative because x is the square of a real expression. he rightly looked at me like I was a little bit stupid. so my mathematical ability is quite low. indeed, that is why I want to study statistics instead.

[bayessays]

I think all of your thoughts are spot-on.  2,3,4 seem like the best letter writers.  You can definitely apply to any top statistics program, and I definitely agree that you don't need to apply lower than UT/Rice range. (Don't know anything about OR)

[baxterbotox]

1 hour ago, bayessays said:

I think all of your thoughts are spot-on.  2,3,4 seem like the best letter writers.  You can definitely apply to any top statistics program, and I definitely agree that you don't need to apply lower than UT/Rice range. (Don't know anything about OR)

Thank you. Do you think it will hurt that only one of my three recommenders will be in statistics? For what it's worth even he isn't really a statistician as his background is in computer science and he mainly works in optimization, just happens to be in a statistics department. Also, the reason I ask about letter writers is mainly because I am not sure who would be better between 1 and 4. The course I took with 4 was in my second year fall, so it has been quite some time, and I don't really interact too much with him as a TA, it's more that I just talk to him if I have any particular questions. That's the only reason why I was questioning if he would be a better choice. Do you think so?

Edited October 5 by baxterbotox
Correct mistake about department

[bayessays]

No, I think stats/math/mathematical CS letters will be viewed similarly by most people.

You didn't have much positive to say about letter writer 1 - does he know you well? Is the research you did with him a huge part of your SOP? You already have 2 letters from research advisors, so I personally think it's totally fine to have a third letter from a math professor who knows you pretty well and you know will write something nice.