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I currently am working on a MS in pure maths, but am interested in options for pursuing a PhD in a more applied field. Specifically I am interested in going on to graduate work in something like statistics. How hard would it be for me to go straight from an MS in pure math with only a very few courses in statistics to a PhD program in statistics?

I have some experience in probability with my research (random walks on finite groups). But outside of that, I am pretty inexperienced with applied math.

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    I'm in the midst of a PhD in biostatistics, and from my experience I think you will do just fine. You might have to take some masters level stat courses to familiarize yourself with some of the basic concepts in statistics. – bdeonovic Apr 25 '14 at 12:17
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    I got into multiple strong statistics PhD programs from a pure math MS having taken two statistics course and one probability course. – Zach H Apr 26 '14 at 20:38
  • Like Zach, I took a small handful of statistics/probability related courses before transferring from a Math PhD program to a Statistics PhD program. – Faheem Mitha May 29 '14 at 8:07
  • Like @Vladhagen (with whom I have talked previously), I, too, am looking to move to a PhD in Statistics/Applied Math. It'd be great if you could perhaps look at my profile and comment on my situation based on your having gone through a similar process. I have created a chat room, chat.stackexchange.com/rooms/97824/…, where I can share more details. – user82261 Aug 24 at 18:03
  • @FaheemMitha ^For you. – user82261 Aug 24 at 18:04
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I think the main hurdle will not be the knowledge about statistics you'll bring. (As a trained mathematician you should be able to pick up new math quick enough.) The main hurdle could be to embrace a new kind of doing science and research.

In more applied math people sometimes think differently about problems than in pure math. Roughly speaking, one is much more open to adapt assumptions and requirements for some problems such that they become more simple theoretically, more suited computationally or otherwise more convenient. Since one usually works with things that are related to the real world and hence, somehow uncertain and noisy, it is often not useful to stick to every assumption but use some freedom in modeling. I heard the saying "All models are wrong." Well, true but this should not make you hesitate to work with models.

I've seen people changing from pure math to applied math who never could adopt to these principles (but also cases where there were no problems). If you think that you won't have problems with issues like I described, then things will turn out fine, I think.

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    The full quote is "essentially, all models are wrong, but some are useful" in: Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley – Maarten Buis Apr 25 '14 at 10:14
  • "embrace a new kind a doing science and research"? Also "requirements for some problems such they become more simple theoretically,". In the latter I think you have a missing "that". – Faheem Mitha Apr 26 '14 at 8:08
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Perhaps another big difference is that being able to interact with other disciplines is very important to be good at statistics. If you are open minded and curious about learning other topics (e.g. genetics, computation, etc), together with a solid mathematical background you can be a very good asset in statistics.

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Math graduates is what most of the body of grad students in statistics is made up of (I've been both a stat student and a stat faculty, so have seen a fair number of these folks). In terms of getting into a program based on your credentials, you wouldn't have any issues (unless, of course, your US-style GPA is like 2.2, in which case you would have some explaining to do in any application to any program, no matter what the discipline is). If anything, you'd be better prepared to tackle the theoretical courses. For instance, the Central Limit Theorem should be proven using characteristic functions rather than moment generating functions, since the latter are not defined for all the distributions to which CLT applies; as a good math major, you probably have had a course in complex analysis. What's more, it might be easier for you to get to a top program, as lower ranked ones may consider you to be overqualified. On the other hand, as other answers strongly suggest, you need to have a more practical mindset than what is typically found among pure mathematicians to get through the applied courses. (The most difficult ones for me were the courses on psychological aspects of response in survey data collection: there was about 5 papers ~ 100 pages worth of reading every week, and the concepts were entirely foreign to me.)

Check out CrossValidated site in the SE system to see what this could be about. (Note that it is heavily biased towards computational/machine learning side of statistics.)

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Modern statistics is pretty computational, which you might not have been exposed to in pure math. I switched from CS to stats and had to play catch up on theory; you might be the opposite, and need to learn how to code.

  • Thankfully I got a minor in CS and work a lot with computational methods currently. Thanks for the heads up however. It confirms what I suspected. – Vladhagen May 13 '14 at 0:15

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