Reasonable range for statistics PhD

[dicerolls]

Hi everyone,

I've recently developed a desire to build a deeper understanding of statistics, partially fostered by some ongoing research I've been assisting in a deep learning lab at my school. I've been setting myself up for a career in industry (quant research) thus far, so it'd be helpful to get an idea of the strength of my profile for PhD programs from you folks. Where do I stand? What can I do from this point on to improve my odds of admission to a program aligned with my interests (currently in reinforcement learning)?

School/year: One of Stanford/MIT/Caltech; currently a junior

Major: Computational Math, Applied Math

GPA: 4.0+ overall and in major

GRE: N/A (1570/1600 on SAT)

Coursework: Standard freshman math (intro real analysis, linalg, and multi); measure theory; intro 1-year discrete math course; upper-level probability and stats; complex analysis; intro ODEs and PDEs; algorithm design; data structures; graduate numerical linalg; graduate numerical methods; graduate markov chains and discrete stochastics; graduate gaussian processes; and currently enrolled in 1-year upper-level real analysis course

Internship experience: Freshman summer as a data science intern at a startup; sophomore summer as a quantitative research intern at a mid-sized options market maker in Chicago; junior (incoming) summer as a quantitative research intern at a large, well-known quantitative market maker/hedge fund

Research experience: Limited, though I have been assisting a professor and his postdocs on a deep learning project this term (and have been encouraged to extend the engagement for as long as desired) in a capacity that is expected to result in a publication within the year, which should be pretty nice

I understand that asking about my chances at the "top-n" schools is somewhat reductive w.r.t. the intricacies and strengths of each department, but it would nonetheless be helpful to get an idea of whether I could be competitive for the top n = 5, 10, 20, 30, etc. Thanks!

[bayessays]

Probably top 5, almost certainly top 10-12. If you're working with a prof on a deep learning project at one of those schools and can get a good letter from him, you're pretty set with your grades, extensive math coursework, and your school pedigree.  Statistics is not like CS where you need publications before applying.