MS Course Suggestions?

[PhysicsKid]

Hey everyone! 

I am about to start a Masters in Statistics at Stanford where there is a fair amount of freedom in terms of what courses to take. I really want to get a PhD in Statistics after my Masters, but took very little Pure Math in Undergrad. I had done lots of Physics and Chemistry, but I think that the lack of Real Analysis on my transcript made it difficult for PhD applications. I really really want to challenge myself and was thinking of trying to take the courses for the intro PhD sequence but I heard on this forum in other places that some places actually view having already taken intro PhD classes as a bad thing for PhD admissions (to my dismay!). My profile in general is a bit weird though so I guess I am just wondering what would look best on a transcript in terms of coursework. I am actively looking to join a more statistics oriented research group after mostly doing research in Physics in Undergrad.

Student Type: Domestic Asian/White Male

Undergrad: Mid-tier Ivy

Major: Physics

GPA: 3.84

Undergrad: Honors Calculus (A), Partial Differential Equations (A), Probability (A), Accelerated Intro to Comp. Sci (B), Graduate Statistical Mechanics (Chemistry) (A), Graduate Statistical Mechanics (Physics) (A), Graduate Quantum Mechanics A & B (As), Graduate Solid State Chemistry (A), Graduate Biological Physics (A)

GRE: 170 Q/ 170 V/ 5.0 W

Research: 3 years of research in Computational Physics and Chemistry labs, no publications but lots of experience applying various ML algorithms with Tensorflow

Other Experience: MITx Statistics (A, but online so I get that it is kinda jank but this was a really rigorous and mathematical intro to Statistics), MITx Data Analysis in R (A, also a great course but was also online), work experience at an AI Cybersecurity firm

I want to go to a very good PhD program in Statistics after my Masters and I had a couple interviews with PhD programs this year (Columbia among others) but didn't get accepted I believe partly because of my lack of real analysis on my transcript. Should I just take fun courses for the required Statistics Courses and not do the intro PhD sequence, make sure I take as much Math and CS as possible and then hopefully find a research position in some statistics or statistics adjacent lab? In terms of the math i should take, would it be weird if I still didn't take their undergrad Honors Real Analysis I class and instead tried to take Lebesgue integration and Fourier analysis (basically their Real Analysis II). Would it make sense to take Math classes other than real analysis? Sorry for all the questions! I really would appreciate any input!

[Stat Assistant Professor]

Besides the required classes for your Masters program (I'm assuming that this entails 2 semesters of Casella & Berger-level mathematical statistics, 2 semesters of applied statistics, and a semester Linear Models), I recommend that you take:

• 2 semesters of real analysis
• proof-based upper-division linear algebra
• one other advanced math class of your choosing, if you can fit it in your schedule (if not, then the 3 math classes above should suffice).

If you can afford it, it may be worthwhile to enroll in a math class for credit at an accredited school over the summer *before* starting your Masters program. That way, you can knock out one of the classes above over the summer and you can take other classes that interest you in your Masters program. Instead of taking PhD-level Statistics classes (i.e. those classes *beyond* the Masters-level, e.g. Advanced Inference or Measure-Theoretic Probability), I agree with previous posters it is a better idea to take statistics electives that interest you and/or more math classes.  

I think if you have at least 2 semesters of Analysis and a semester of proof-based linear algebra, you should see good results for PhD admissions in Statistics. A 3.84 GPA in Physics (a tough subject!) from an Ivy is definitely nothing to sneeze at. Those factors --plus strong performance in a Masters program and A's in two semesters of Analysis -- should put you in great shape to get into a good Statistics PhD program. I'm not sure if it will guarantee admission to Columbia, Harvard, or Stanford, but I wouldn't be surprised if you get into say, University of Washington, University of Michigan, or Duke (assuming that you perform well in your Masters program and take the classes above). 

Edited May 1, 2021 by Stat Assistant Professor

[DanielWarlock]

I would recommend just taking same courses with PhD students at Stanford (probability, theory stats, and applied stats) and focus on doing research. If you could do PhD sequence, there is no concern about whether or not if you have real analysis. And this saves you tons of time when you become a phd because you have already done these classes. 

I think you failed last time because you have no relevant research experience in statistics--that *in principle* is fine but you are competing against people who have done cutting-edge stuff in stats for 2+ years in their undergrad and have accumulated quite a bit of expertise. At Harvard at least, most people come in with prior concentration on one of the subfields, say experimental design/causal inference, Bayesian computation, network data, differential privacy/minimax bound etc. It helps a lot when you have substantial letters from experts who work in your chosen subfield. This doesn't mean they published in top journals--just that they demonstrate interest and research experience in these things. 

If I were you, I would find say Montanari (who is also a physicist turned statistician) and start doing research on AMP/deep learning/spin glass right away. I could say with very high confidence that you can get admission from the departments that have interests in this area, e.g. Yale, Chicago, Stanford, Berkeley, Columbia, MIT (math). The reason? Not a lot of undergrads have worked in this area or even know anything about it. A physics-major from Stanford stats with a letter from Montanari/Chatterjee would look very,very good to top departments. This is just one example. Usual high dimensional stats is probably a safer choice and a letter from Candes probably will make competitive anywhere. But I would say it's a lesser strategy because there will be a lot of competition from peers with similar interests. 

I stress that you don't need to publish in top journals or have solved some open problems. Just exposure + experience is fine. Statistics, and probably academia in general, cares a lot about pedigree even at undergrad level. *Substantial* letter from famous scholars is the most effective way to stand out. 

No need to obsess with real analysis or courses in general. I think it has very little impact when your goal is top 10 departments. Usually lower-ranked departments care more about it so that they can make sure the admits can handle first-year class. 

 

 

 

Edited May 2, 2021 by DanielWarlock