What is the preferred route for someone interested in Probability Theory, a Math or a Stats Department?

[Radon-Nikodym]

Like the title states, my question is whether a mathematics or statistics department would be better to study and ultimately do research in probability theory. My interests are mostly in things like random graphs, random matrices, stochastic processes, and other related topics (the theory side rather than the applied side). I've applied to both statistics and mathematics departments that have faculty working in these areas, and I am wondering if I ultimately have to decide between the two, which one would be the preferred route? My current goal is to end up as a tenure-track faculty member, but I know how difficult and unlikely this outcome can be. 

To make my question more concrete, I guess I'm asking: What are the advantages and disadvantages of pursuing research in probability theory in a math department vs. a stats department?

Edited January 10, 2018 by Radon-Nikodym

[Stat Assistant Professor]

As long as your PhD advisor is a reputable name in the probability theory community and matches your interests, then I don't think it matters so much whether it's in a Math or a Stats Dept. There are some Statistics (as well as Computer Science and Operations Research & Engineering) departments that are very strong in probability theory. If your interests are primarily in probability, then you are almost certainly going to need to do a postdoc, so the choice of advisor is absolutely crucial for securing a good postdoc after you graduate (whereas in Stat/biostat, you can sometimes get away with not doing one if you have at least one article accepted in a top journal as a grad student). Moreover, the top schools in Statistics (like UC Berkeley) have a specific plan of required coursework for students who are interested in probability theory, so you are certain to take the necessary classes needed to conduct research  in a stat department (e.g. UC Berkeley Statistics would require you to take the 2 semesters of analysis/measure theory and some other relevant classes from the math dept).

 

 The main difference would probably be the coursework requirements. In math departments, you'd be required to take abstract algebra and topology (maybe multiple semesters of these), but not necessarily any core stat classes like theoretical statistics, regression, linear models, categorical data analysis, etc. That's not really a problem from a research perspective -- most of the learning you do in grad school is teaching yourself through reading papers, conducting your own research, etc. But the coursework requirements for your personal  knowledge/edification are something to consider.

[Radon-Nikodym]

Thanks for the advice! One thing I've heard is that getting a tenure-track position is easier in Statistics than it is in Mathematics. Is this also the case for those in a Statistics department focusing mainly on probability theory or more theoretical topics in Statistics? Another thing I've heard from several sources is that it is significantly harder to be accepted to a top mathematics program than it is a top statistics program, as the competition for the top 10 mathematics programs is intense (I applied mostly to top 10 statistics programs but I applied to mostly programs ranked around 10-15 in math). I've heard that higher-ranked programs correlate strongly with finding a good postdoc position, so will both of these have similar outcomes, or will one have slightly better outcomes than the other? Also, is it possible for a Statistics PhD to get a postdoc in math department, or vice versa? 

I was also wondering about the culture of Statistics vs. Mathematics departments. For instance, I get the impression that Statistics PhD students are not quite as interested in theory as Math students. Looking through the profiles of students in Statistics departments, it seems that the vast majority of them are listing research interests in methodological/applied areas rather than theoretical topics, and I couldn't find too many that are explicitly interested in mathematics topics like probability theory. I'm a little worried that if I go to a Statistics department, I'll have a hard time relating and discussing my research interests with the other students, while I'm fairly confident that I will have a lot of shared interests with students in a Math department. Is this a valid concern, or am I overthinking this?

Edited January 14, 2018 by Radon-Nikodym

[Stat Assistant Professor]

1) The job market for (pure) mathematics is definitely tougher than it is for statistics. It is still possible to secure a tenure-track job in a Statistics department without doing a postdoc (although it's becoming a lot tougher now), but this is virtually unheard of for mathematics. As a reference, even Mathematics Professor Daniel Kane -- who publishes a gazillion papers in both pure math and theoretical computer science -- did a postdoc.

2) I am not sure about the competition for a top mathematics program vs. a top statistics program, but it is still fairly competitive for Stat. In the Statistics program I'm graduating from in August, they accept around 15-20 students a year out of roughly 200 applicants. Other schools have similar statistics (e.g. on the Stanford FAQ page, it indicates that they admit 10-12 students out of 120 applications, and it's probably similar at other top-tier statistics departments).  

3) For securing a good postdoc, the PhD advisor matters far more than the pedigree (although the latter is also taken into account). I don't think that any math OR statistics department is going to frown upon someone who had Persi Diaconis (in the Stanford Statistics department) as their advisor -- someone who had Diaconis as their advisor can definitely get a good postdoc in a mathematics department. Also, there certainly is a strong correlation between pedigree and success on the job market, but I suspect it's because there are more choices to pick from in a highly ranked department. But in the end, the most important thing is that your advisor is someone who is active in the field, well-connected, and most importantly, someone whom you can get along with (I think this last point is pretty crucial and something that a lot of students who are "starstruck" don't consider nearly enough). 

4) Re: culture. You will find people interested in a variety of topics in any math or stat department. My work is mainly theoretical (as in theorem-proof type stuff). There are other students in my department who are predominantly interested in theory as well. For example, the students who work on Markov chain Monte Carlo theory in my department are doing some very abstract stuff with functional analysis. The same would be true in a mathematics department, where you'd probably have both applied mathematicians and pure mathematicians. I think you should visit the places that you are accepted to and then you can better assess culture and personal fit.

Edited January 14, 2018 by Applied Math to Stat

[Radon-Nikodym]

I was just admitted to Berkeley Statistics! I'm so incredibly relieved, given that my own department (UChicago) has been keeping me in the dark. So now I guess I actually have to make the decision of whether I want to spend my next 5+ years in a Statistics department or a Math department. So far, I've also been accepted to UCLA and Michigan Math, which are fantastic programs as well. This will be a really difficult decision...

Edited February 8, 2018 by Radon-Nikodym

[Jiageng]

1 hour ago, Radon-Nikodym said:

I was just admitted to Berkeley Statistics! I'm so incredibly relieved, given that my own department (UChicago) has been keeping me in the dark. So now I guess I actually have to make the decision of whether I want to spend my next 5+ years in a Statistics department or a Math department. So far, I've also been accepted to UCLA and Michigan Math, which are fantastic programs as well. This will be a really difficult decision...

I am from UCLA and Professor Georg Menz here works on probability after finishing a postdoc at Stanford. Since you have been admitted, it might be a good idea to email him and ask. Congrats again Radon-Nikodym :-)