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I am a Mathematics student with a concentration in Applied and Computational Mathematics. I have done a Mathematics research project with a faculty member, which resulted in a co-authored paper being refereed. This project was on image processing, and I was exposed to some large scale data analysis. The original knowledge discovery element of the project was very exciting, and that's what made me decide to go to graduate school.

However, I had a hard time deciding what I want to study. I am naturally interested in many things (I was an Art History major before switching to Mathematics), and not inclined to put forth serious intellectual effort in anything that would narrow my career possibilities afterwards. For example, for some time I was very interested in Financial Mathematics, but then realized that this may limit my career options to the finance industry. With my research experience, I could see that Data Science is an interdisciplinary subject with potential application in a vast number of fields. So Data Science is a possible "major" for my graduate study.

As for the programs, Master programs bearing the names of "Data Analytics", "Data Science" and the like don't appeal to me as much as Statistics MS/PhD with Data Science track. The reason is that many of the former ones seem to be more or less "fad" programs (I'm not wishing to offend anyone here, so correct me if I'm wrong) designed to meet increasing industry demands for skilled data analysts, and so may lack the systematic, deep mathematical rigor and generality (i.e., not confined to business applications) I appreciate in the latter programs.

So it seems a PhD/Master in Statistics would suit my criteria for (1) a widely applicable, interdisciplinary subject and (2) more rigorous, mathematical training of the subject. What do you think?

Please note that as of now I have no particular preference for industry or academia after program completion. Which of the two I will end up in will depend largely on how my job search goes. I know that the number of faculty positions is much fewer than the number of PhD students wishing to fill those positions; also industry may pay better, and I am not dead set on producing academic papers in prestigious journals. As long as I get to work on interesting problems, using data science as a tool, and make independent discoveries as contribution, I would be happy.

Edit: Since this post may be too broad, as @Stephen pointed out, I rephrased my question as follows: given my interests in (1) independent knowledge discovery, (2) diversity of knowledge domains and applications, (3) systematic training, and (4) a career in Data Science, my question is: Is a Ph.D. in Statistics the right path? @Stephen has given a thoughtful response, but I would like to hear from others as well.

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    There are three elements to being an effective Data Scientist: 1. a solid grounding in Stats; 2. a good grasp of Data Structures and Algorithms; 3. Enough solid communication skills and enough domain background to work effectively with the problem domain experts. – Vietnhi Phuvan Dec 19 '14 at 1:30
  • Attend a master programme/PhD that you like, above all, and that is broad - mathematics, physics or the like - without focusing too much on the name. Most data scientists are either mathematicians or physicists by education (I, too, for example) plus knowledge of coding languages and machine learning (and you can easily get meanwhile you study). – gented Oct 5 '16 at 13:28
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Interesting question, but likely to be closed as "opinion-based" or "too broad".

I personally have a math Ph.D., then started to do applied statistics in a "classical" academic environment (analyzing psychology studies), finally ended up in a Data Science-type job. I fully agree that postgraduate work in statistics would be the best preparation for a career in Data Science.

As @Vietnhi notes, there are three key ingredients for becoming a good Data Scientist:

  • a solid grounding in statistics
  • programming/hacking skills
  • subject matter expertise

(See also Drew Conway's Data Science Venn Diagram, which I posted and discussed here).

Of the three, it seems to me like the statistics part is hardest to learn in a non-structured environment. From what I see in my day-to-day work and on CrossValidated, people will rather easily pick up programming skills and subject matter knowledge, but understanding randomness - and this is really what statistics is all about - is very hard. (See, e.g., here.)

So as long as there are no serious Data Science study tracks available (and I agree that most offerings right now are likely bandwagons people jump on), it makes sense to concentrate on statistics (getting a structured study path via the Ph.D. program), but really work to understand the actual tools for handling large data sets, and trying to get a certain amount of subject matter expertise in at least one field. Optimally, you'd do an applied stats thesis which requires you to actually work in a specific field and apply stats there.

You may want to look at Data Science.

  • @Stephen Thank you very much for your thoughtful response to my inquiry and various helpful pointers. One more question: would a Ph.D. in an Applied Mathematics department with a focus on Statistics (e.g., John Hopkins Ph.D. program in Applied Mathematics & Statistics) give one a level of statistical expertise comparable to that in a Statistics department? By statistical expertise I mean the understanding of randomness, like you mentioned in your post, as well as the underlying mathematical maturity. "Comparable" can mean either "more" or "less". – user90593 Dec 19 '14 at 12:59
  • Sorry, but I can't answer that question, I have no idea. I suspect that the difference in programs would be dominated by the difference in participants, i.e., even if program A teaches you more than program B, you may still find in comparing single graduates from both programs that a random B graduate knows more than a random A graduate, based on emphases in coursework etc. But as I'm saying, I'm just guessing. Sorry. – Stephan Kolassa Dec 19 '14 at 13:05
  • I was going to write an answer, but I don't think I can improve on Stephan's excellent answer, which covers all the main points. If I do think of something else to say, I'll write an answer. With regard to your followup question, I, like Stephan, have no idea. However, here are some obvious suggestions. First talk to JH (for example) directly with regard to your concerns. They are the best places to answer your questions. Second, you should also take a look at their PhD course requirements if you have not done so already. – Faheem Mitha Dec 20 '14 at 8:32
  • One concern is that an applied math program may force you through coursework which you may not be interested in and have no use for. This is a potential problem with any PhD program - in my experience they all have coursework which is a waste of time - but it may be worse in an applied math program if what you are really interested in is Statistics. – Faheem Mitha Dec 20 '14 at 8:33

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