# Subfields of Statistics?

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Hey all. I'm an undergraduate who's looking to apply to Ph.D programs in Stats in a couple years. I know this isn't necessary to know yet, but I'd like to have a good understanding of the subfields of Stats. It seems a bit opaque to me as of now. With a subject like math, when looking through professors' profiles there seems to be a list of about 10-12 broad research areas that people study (algebraic geometry, PDEs, number theory, etc.). Within stats, the research interests I see paint a less-clear picture. Also, level of detail tends to vary (a professor might list their research interests as "mathematical statistics"). In browsing through some profiles I've compiled the following list — what am I missing? Is there a resource you would recommend to become more familiar with the breakdown of subfields? Is there a reason for a less-clear hierarchy of stats research interests (when compared to math)?

• Applied Statistics
• Biostatistics
• Statistical genetics
• Statistics X Neuroscience
• Functional data analysis
• Statistics X Finance
• Statistics X Social Science
• Longitudinal analysis
• Causal Inference
• Theoretical Statistics
• High-dimensional statistics
• Non-parametric/semi-parametric statistics
• Statistical learning
• Bayesian statistics
• Signal processing
• Harmonic Analysis
• Probability Theory
• Stochastic processes

This is the broad breakdown that I would make based on my current knowledge but I would like to know if this is missing anything major and/or if you think understanding the breakdown of the field is even helpful. Also, I'm sure there is nuance not included above (I assume there is a lot of applied Bayesian work and theoretical causal inference) but this is my broad understanding. Please correct me!

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Pure probability research is generally pretty rare in statistics departments outside of a few departments.  For statistics research, people generally divide it up into applied research (answering questions), methodological research (creating new statistical methods) and theoretical (proving mathematical things about methods).  Most statisticians do some combination of more than one of these, and a large amount of the research you'd do in a PhD program would likely be some combination of methods and theory research, with maybe some applied work especially if you're in a biostatistics program.

For application areas, obviously statistics can be applied to almost anything so just look for applied areas that interest you - if you name it, you can probably find it.  For methods, there are too many areas to list - causal inference, high dimensional, Bayesian, survival analysis, functional data, spatial, networks, a million more.

The exact subdivisions aren't as important in statistics as in math because it's much easier to move between fields and work in multiple fields.   You seem to be getting a decent idea of what's available in a lot of departments - so find a department that has a few people who seem to be doing something interesting and don't worry too much about being boxed in.

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I think @bayessays hit the nail on the head. I would hesitate to call statistical genetics applied. The vast majority of work being done is methodological--coming up with new methods to find genes, etc.

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I don't have a clear answer to this. But I just want to comment that it can become extremely broad. For example, I recently discovered that Chatterjee at Stanford even works on quantum field theory! (https://statweb.stanford.edu/~souravc/qft-lectures-combined.pdf) It makes sense in that a lot of statistics come from physics. But eventually I think people just do things because they find them interesting.

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I am also starting to discover the connections between probability -> statistical physics -> spin model -> quantum field theory (arrows not necessarily in that order:P). Chatterjee at Stanford is more of a mathematician in my eyes, not really a statistician. But yes, interesting to think of the side of stat that comes from physics. And be able to use it to approach ML from a different perspective.

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4 hours ago, MathStat said:

I am also starting to discover the connections between probability -> statistical physics -> spin model -> quantum field theory (arrows not necessarily in that order). Chatterjee at Stanford is more of a mathematician in my eyes, not really a statistician. But yes, interesting to think of the side of stat that comes from physics. And be able to use it to approach ML from a different perspective.

I actually digged into the origin of Chatterjee's lecture notes as it is still quite bizzarre that he comes to know so much physics out of nowhere. It turns out he was following a set of notes by Talagrand himself who took up learning quantum field theory as a hobby after turning 60 year old. In the preface of those notes, Talagrand described his frustration of learning physics as a mathematician which is quite funny.

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