Recommendations for former math student switching to stats? Particularly interested in uncertainty quantification, compressed sensing / signal detection, machine learning, manifold learning.

[open_ball]

Here are my stats:

• 3.97 GPA; major: applied math / statistics 
•  Interests: uncertainty quantification, compressed sensing / signal detection, machine learning (broadly speaking), dimension reduction / manifold learning. 
• Relevant coursework: real analysis I and II (my favorite courses I took in college!), numerical analysis, mathematical statistics and probability (2-course sequence), graduate numerical linear algebra course, ODEs, data science programming, cloud computing, ... (all As). Have taken reading courses on probabilistic machine learning, deep learning. Courses left to take: PDEs, regression analysis, graduate real analysis, differential geometry. 
• T25 undergrad (not known for math)
• Female domestic applicant 
• Other notes: I switched from English major, originally was on pre-law track. 

Research experience: all tangentially related to healthcare applications, all related to machine learning. 

1. Math REU (NSF funded) (topic: computational math-- diffusion model). Paper approved for publication in SIAM undergraduate journal
2. Math REU ( (NSF funded) at top public school for applied math (topic: harmonic analysis / machine learning for signal processing). Have not finished arXiv preprint yet
3. Machine learning research assistant (topic: uncertainty quantification). Will be one of the last authors on a paper. 
4. Honors thesis. Topic: have not decided yet. 

Schools I will be applying to:

• Duke stats
• Rice stats
• Northwestern stats
• Columbia stats
• NYU stats 
• UPenn (Wharton) stats
• Yale stats
• University of Washington stats
• Harvard stats
• Stanford (I am really interested in Emmanuel Candes's work on conformal prediction as well as compressed sensing, but I'm probably not good enough). Two other girls from my school / department who graduated in past years got into ICME at Stanford. An operations research prof at Stanford looked over my CV and suggested I apply to ICME.
• REU #2 school (program: applied math / scientific computing) 
• Columbia biostats
• Harvard biostats (Dare I apply???)
• CU Boulder (applied math)
• Columbia (applied math)
• Rice (applied math)

Recommenders: 

1. My PI (has ties to Biomed engineering, CS, and stats department at one of the schools I've listed); tenured
2. Math professor from REU #1; tenured
3. Math professor from REU #2 -- works in applied harmonic analysis; tenured. 

Languages:

LaTex, Python (specifically PyTorch), R, MatLab. 

My question: Which programs are unrealistic for me to apply to?

Am I qualified to apply for biostatistics if I have taken almost no biology/science classes in college? My past research has been related to biomedical applications. 

[bayessays]

Biology/science classes are completely irrelevant to applying to biostatistics programs.  You can realistically apply to any statistics or biostatistics program.

Your list is a little bizarre in that you have a huge gap in terms of school quality.  Your schools are almost exclusively the hardest programs to get into in the top 10, and then you have Northwestern and Rice. I think Rice is about the lowest you should be applying to, but I'd apply to more schools in the 10-30 range because the top 10/Ivys are hard to get into.

You can definitely apply to Harvard biostat and any other biostat program - I'd apply to Harvard/Hopkins/Washington (unless you'd rather do Stat at these schools).

You're selling yourself way short - you literally have the ideal background and my guess is you'll have multiple options in the top 10.

[open_ball]

Thank you for the advice. Can you tell me more about what schools in the 10-30 range I ought to consider? I spoke with one of the only stats professors at my school and he gave me some suggestions. Another issue is that my partner is also applying to PhDs (only on the east / west coast) and we would like to end up close together. 

[bayessays]

Hard to say because it depends on your research interests - you'll have to go to the webpages and look through the professors.  Your interests are pretty niche - "uncertainty quantification" is not a common term for a research field in statistics departments (most statisticians would be confused since the whole field is about uncertainty quantification), there are probably only a few people researching manifold learning (depending on how you define the field - I've only seen manifold learning in CS departments, but there are a few statisticians doing statistics on manifolds with differential geometry and stuff), and I don't think there are many compressed sensing people in stats departments outside of Stanford and maybe a few other top departments that get Stanford grads for faculty.  On the other hand, machine learning is a very broad interest so you'll really just have to dig through faculty profiles and find out where you have a few people you find interesting.

Again, your profile is fantastic, so apply anywhere you want that seems interesting.

[PhysicsKid]

You have a great profile and I wouldn't be surprised if you got into Stanford (or any of the other schools on your list). I would say that if you are specifically interested in Emmanuel, he generally has only taken students from the Stats department (or who come with a very very high recommendation from a friend e.g. Stephen Boyd, Michael Jordan). Of course there are lots of wonderful faculty affiliated with ICME who take ICME students, but it is definitely a more direct path to go into Stats.