Recommendations for programs in "unconventional" areas of theory

[PluvianSprite]

I am currently working in industry, having recently completed a MSc in probability, but I am looking to apply for US Mathematics/Statistics PhD programs in a few years' time. At the moment I'm trying to

• gauge feasibility for certain places in the US based on a rough profile; and
• further build the list of research areas or places in the US that I'm considering.

My current progress is below. Any assistance would be greatly appreciated!

Research areas

My interests are mainly theoretical areas in probability or mathematical statistics rather than applications. I'm particularly fascinated by areas that have emerged due to shortcomings in traditional or conventional methods. I'm also interested in areas that offer alternative perspectives on common problems.

Some examples are

• extreme value theory and heavy-tailed phenomena
• time series
• Bayesian nonparametrics
• information theory
• survival analysis

One other thing: I am not very familiar with the use of probability theory in mathematical physics, even though it seems to be a major research theme in probability in the US. I'm mainly sticking to theoretical areas of probability or stochastic processes that are more aligned with statistics, engineering, and operations research.

Departments I'm considering already

These are mainly inspired by having identified particular members of faculty that I might be interested in doing research with, although there are certainly some that I'm considering simply due to the overall strength/reputation of the department.

• Cornell — Operations Research and Information Engineering
• Columbia — Statistics
• Duke — Statistical Science
• Stanford — Management Science and Engineering
• UC Davis — Statistics
• UC San Diego — Mathematics
• Yale — Statistics and Data Science
• UNC at Chapel Hill — Statistics and Operations Research
• Stanford — Statistics
• UC Berkeley — Statistics
• Chicago — Statistics

Would love any suggestions here!

Brief profile

Institution: One of the top Australian universities (same place for both undergrad and masters)
Major(s): Probability Theory
Minor(s): (notionally) Statistics, Actuarial Science
GPA: We use a different scale but something like a 3.9/4.0 or above maybe

Type of Student: International Asian male

GRE General Test: Have not sat
GRE Subject Test in Mathematics: Have not sat

Research Experience: Masters thesis turned into a preprint. Before that I did a 4-week undergrad project on fractional Brownian motion.
Awards/Honors/Recognitions: Top masters student among those specialising in probability or statistics.
Letters of Recommendation: Should have three from faculty in probability theory. Have taken two or three classes with all of them; one supervised me for my masters thesis, and another was involved in grading my masters thesis.

Maths Grades:  Have no idea how the grades or class names translate, but I took all possible probability classes. I'm guessing something like the following:

Probability and Stochastic Processes (A+); Stochastic Processes II (A+); Probability Theory (A); Stochastic Calculus (A+); Stochastic Processes III (A+); Probability Theory II (A+);

Calculus I–III (A+); Real Analysis (A+); Complex Analysis (A+); Topological and Metric Spaces (A+); Measure Theory (B)

Linear Algebra (A+); Group Theory (A+); Rings and Fields (A+); Commutative Algebra (B+)

Statistics Grades: Mathematical Statistics I (A+); Linear Models (A); Survival Analysis for Actuaries (A); Generalised Linear Models (A); Mathematical Statistics II (B+); High-Dimensional Statistics (A+)
Any Miscellaneous Points that Might Help: About 1/4 of those subjects listed above were masters-level courses here, which roughly corresponds to upper-division undergrad classes or first-year graduate classes in the US.

[Stat Assistant Professor]

I wouldn't say that any of your research interests are particularly "unconventional," but that aside, I think your list of schools is good given your interests, and I think you stand a good chance of getting into some of those schools with your profile. Scoring well on the Subject GRE would also help a lot at some of the top schools on your list.

I can't think of any other schools to recommend off the top of my head, but a good idea when researching departments is to see if there are enough faculty publishing in mainly theoretical journals like Annals of Statistics, Annals of Probability, Journal of Theoretical Probability, Bernoulli, Stochastic Processes and Their Applications, and IEEE Transactions on Information Theory (other stat journals like JASA, Biometrika, JRSS-B also contain theory but these also tend to place a big focus on methodology, applications, computational/implementation aspects as well, whereas the other aforementioned journals are often mainly theoretical -- often times, there are articles published in Annals, Bernoulli, etc. that don't contain any simulation studies or applications on real data).

Edited April 19, 2019 by Stat PhD Now Postdoc

[PluvianSprite]

Thanks for the reply @Stat PhD Now Postdoc. In the grand scheme of things, these research areas are certainly not genuinely unconventional like you said, but they are unfortunately not the hottest topics right now (maybe aside from Bayesian nonparametrics).

I'm also curious about the feasibility of applying to mathematics departments, since many tend to house some probability faculty. Is it usual for admissions committees to separate applications by desired research field before judging them? In the sense of resource allocation at least, would a prospective student in probability usually need to demonstrate greater merit/potential compared to other applicants interested in analysis/algebra/geometry in order to receive an offer?

[Stat Assistant Professor]

You could certainly apply to mathematics PhD programs with your profile and the breadth of classes you took. Score well on the Math Subject GRE and you could probably get into a respectable math program. If that is your wish, then definitely ask for a recommendation letter from the professor who supervised your Masters thesis that you turned into a preprint. I don't think the admissions committees in Math departments separate the applications based on desired research field (nor do Statistics departments). You can mention individual professors with whom you would like to work in your statement of purpose, so your application might be passed along to them to take a look at and offer their opinion. But they won't be the ones accepting you - the admissions committee will be. 

One thing to consider about Math PhD programs is that the coursework would be quite different from ORIE or Statistics (i.e. in the first year of a Math PhD program, you'd have to take two semesters of Abstract Algebra, two semesters of Analysis, Topology, and Complex Analysis, and then in your second and third years, you have a bit more freedom to choose classes in your specialty).