dm_stats

Hello all,
Just wanted to update you guys who helped me on here that I have made the decision to go to UW. @Stat PhD Now Postdoc and @Cavalerius thank you so much for helping me out, your advice and input was truly invaluable and incredibly informative. I wish you both the best!

Hello all,
Just wanted to update you guys who helped me on here that I have made the decision to go to UW. @Stat PhD Now Postdoc and @Cavalerius thank you so much for helping me out, your advice and input was truly invaluable and incredibly informative. I wish you both the best!

Hello all,
Just wanted to update you guys who helped me on here that I have made the decision to go to UW. @Stat PhD Now Postdoc and @Cavalerius thank you so much for helping me out, your advice and input was truly invaluable and incredibly informative. I wish you both the best!

It is interesting because given the description that I cited of the various fields, I would definitely have thought that operations research rather than statistics would be the more obvious fit for my own research interests: My background has been heavier in pure math than in computer science or applied math, and my primary interest--although I am trying to remain somewhat flexible on this point--is in topics that lie at the intersection of statistics and finance. Thus, I looked at the programs to which I'd been accepted and the opportunities that each provided for me to do research in statistics that would also be relevant to finance in particular, and it seemed that while operations research and areas like stochastic calculus are mathematically rich and pertinent to mathematical finance, more promise was held (for both academic inquiry and for industrial applications) by some of the newer methods and tools being devised in statistics and machine learning. Moreover, given my predisposition to finance, I looked at how closely aligned each school's statistics program was with its business school (through shared classes, dual appointments, presence of faculty on dissertation committees, etc.) as well as the quality of the business school.
After accounting for the strength of research fit, I also made by decision based on the location of the school, the funding package and related responsibilities, and the structure of the program (e.g., the number of required classes, size of the program, and accessibility of professors).
 
Anyway, I am not sure whether any of this information is helpful in your case, but right or wrong, that was my thought process. (It was without a doubt one of the tougher decisions that I have had to make in my academic career thus far. I am sure given the quality of the programs in question that you've worked very hard to have these opportunities, and you want to ensure that you are making the best decision to both reap the benefits of your work to this point and set you up for future success, so it is certainly a difficult decision to make.)

You could take a quick look through the publications and preprints of these faculty members and try to get a sense of which department is more appealing to you. If you are interested in applying mathematical tools from geometry and topology to statistics/ML and there are more faculty working on this at UW than at Princeton -- and said faculty are also publishing in top journals (like Annals of Statistics, Annals of Applied Probability, JASA, JRSS-B, Biometrika, IEEE Transactions, etc.) and top conferences (like ICML, NeurIPS, AIStats), then I would think that UW is a better fit than Princeton. But only you can decide which is better for yourself.

Although I did not apply to any of the schools that you mention (or to Cornell either, for that matter), I also had to choose between operations research and statistics and found the following description on Cornell's statistics PhD website to be helpful:

Choosing a Field of Study
There are many graduate fields of study at Cornell University. The best choice of graduate field in which to pursue a degree depends on your major interests. Statistics is a subject that lies at the interface of theory, applications, and computing. Statisticians must therefore possess a broad spectrum of skills, including expertise in statistical theory, study design, data analysis, probability, computing, and mathematics. Statisticians must also be expert communicators, with the ability to formulate complex research questions in appropriate statistical terms, explain statistical concepts and methods to their collaborators, and assist them in properly communicating their results. If the study of statistics is your major interest then you should seriously consider applying to the Field of Statistics.
There are also several related fields that may fit even better with your interests and career goals. For example, if you are mainly interested in mathematics and computation as they relate to modeling genetics and other biological processes (e.g, protein structure and function, computational neuroscience, biomechanics, population genetics, high throughput genetic scanning), you might consider the Field of Computational Biology. You may wish to consider applying to the Field of Electrical and Computer Engineering if you are interested in the applications of probability and statistics to signal processing, data compression, information theory, and image processing. Those with a background in the social sciences might wish to consider the Field of Industrial and Labor Relations with a major or minor in the subject of Economic and Social Statistics. Strong interest and training in mathematics or probability might lead you to choose the Field of Mathematics. Lastly, if you have a strong mathematics background and an interest in general problem-solving techniques (e.g., optimization and simulation) or applied stochastic processes (e.g., mathematical finance, queuing theory, traffic theory, and inventory theory) you should consider the Field of Operations Research.

I don't think you would be a disadvantage in the academic job market if you had a PhD in Operations Research, particularly if the degree is from a school as prestigious as Princeton. Hiring committees (at R1's) care more about your publications and your ability to do high-impact work (assessed from recommendation letters and your presentations at conferences) than about what your degree is in.
In theoretical statistics and ML, you definitely do use tools from pure math to prove theoretical properties of statistical models. Some subfields of stat/ML make heavy use of geometry and combinatorics. Others, like functional data analysis, need to use tools from functional analysis and Hilbert space theory. But statistics is still mainly an inferential field (making predictions and estimating unknown parameters and functions from data), and the emphasis is not on the most fundamental objects (like the probability space itself or the random variables/collections of random variables themselves) like in probability theory. 

Princeton's ORFE Department could certainly lead to a great academic career in a Statistics/Math Department, especially if you work with Jianqing Fan who is quite famous and productive. However, one thing to consider is that apart from Fan, it seems as though the OFRE Department at Princeton focuses more heavily on probability theory and stochastic processes than UW, which seems to focus more on statistics and machine learning. While there is definitely overlap between these areas (after all, probability is the basic foundation of statistics), I would say that probability is more of a branch of pure mathematics and "fundamental science" than statistics. Every Statistics Department has a couple of probabilitists though.  
I would consider how much you enjoy probability theory and pure mathematics. If you are really into that, then Princeton OFRE may be a better choice. If you are more interested in statistics and machine learning (including the mathematical/theoretical foundations of statistical/ML models), then UW still may be the better fit.