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I'm in the second half of an electrical engineering doctorate but have come to realize that mathematical statistics and the theoretical side of information theory might be more my calling. I am too far along in my research to pivot my doctoral thesis to this abstract of an area, especially considering I am in the engineering department.

I am relatively strong in math (Tall for a hobbit... taking the grad functional analysis sequence, albeit late relative to when math students see it) and have a (very conservative) original math side project, so I believe I am at least capable of understanding math research. However my environment is still most conducive to studying engineering problems, not math/stats ones.

If someone in this position wanted to research and publish in mathematical statistics later on, would an engineering doctorate be enough credentials to do so?

There are several reasons I ask:

  • The amount of math knowledge implied by a typical engineering doctorate is not anywhere near the amount necessary to do research in statistics theory. (Not to say the EEs I have met here aren't extremely capable in their field, just most aren't focused on research level math).
  • The direction my adviser and I are headed with my current thesis is interesting and useful. I'm not about to drop my engineering degree.
  • If it isn't necessary I would rather not jump through all the hoops of getting a PhD all over again.
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    To publish research, you don't need credentials. You need significant results. – David Ketcheson Sep 15 '16 at 7:01
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    Quick clarification question: Are you asking whether you would be able to acquire a position where your focus was research related to statistics or whether you can publish in this area? No credentials are required for publications. – user58322 Sep 15 '16 at 7:04
  • Is it possible to use statistical concepts and theories in your phd works? – Hadi Sep 15 '16 at 7:25
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    While simply being able/allowed to publish won't really be an issue, I wonder if your question is rather how will it effect your ability to be employed in a position that encourages you to do this research? You could always do it on the side and try to publish, but that's very different than trying to get a job (academia or industry) where you are allowed and encouraged to work in the area you want to work in. But I don't want to put words in your mouth or just guess, but you should at least consider that's a different question with possibly different answers. – BrianH Sep 18 '16 at 1:12
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No formal credential is required for scientific publication in any discipline.

What is required is good work, presented well in a context in which the reviewers can understand your results and their significance to the community with which you are communicating.

That often strongly correlates with having a Ph.D. in the discipline in which you are publishing, since that is the most straight-forward manner in which to acquire the skills and knowledge necessary for effectively engaging with such a community. There are many other ways to get engaged with a scientific discipline, however.

For example, you're coming up on another good opportunity for shifting between communities, however, which is getting a postdoc in the area in which you work. Given what you have described of your situation, I would suggest following through to completion with your Ph.D. work, while simultaneously continuing to explore your alternate interests and looking for a good postdoc to help you shift.

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As stated in other answers, doing a postdoc in your newly-found area of interest after finishing your PhD would be the preferable way to switch your focus.

While I essentially agree with most of the other answers, I want to mention here that your plan may not be as far-fetched as you think it is, or as others would have you believe. Your target areas (mathematical statistics and theoretical information theory) are studied by electrical engineers, and there is no need to switch from EE to other fields of study entirely.

Choosing your postdoc institution wisely is the key to success. If you are not inclined to toss aside your EE credentials completely, and still don't mind being aligned with (gasp!) electrical engineering (who says EE isn't great?), one thing to look for are EE departments that have more theoretical leanings. Some schools that come to mind here are Stanford, UC Berkeley, UCSD, Duke, UT Austin, UIUC, Caltech, Georgia Tech, Columbia, and Princeton. Schools that combine their electrical engineering and computer science faculty into one department also would be worthwhile to investigate.

Just to give you some ideas of where to look, here are some researchers who are either EEs, or are affiliated in some way with EE departments, and do the type of research that you want to get into:

Additionally, here are two researchers who did their PhDs in EE, but are now faculty in statistics departments:

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If you are interested in staying in academia, do a postdoc. You have a new interest that extends your grad work, but that you don't have precisely the right background to drop into the field without additional training. I'd describe this as almost the ideal situation for starting a postdoc! Look for someone a bit more embedded in mathematics with research interests in the direction you're interested in. With your engineering background, you could bring new problems or new techniques to them. Unless you are dealing with work that needs massive amounts of analysis and measure theory, I think many applied mathematicians would be happy to work with people with slightly different backgrounds, especially if you can make a case to them that you have gone through the coursework. [As a warning: there can be some cultural transitions - many math postdocs teach to support themselves!]

If you are not interested in staying in academia, and just want to publish because you find the work interesting - then credentials don't matter as much. But you still might want to get a little connected to people just to see if 1) your questions are interesting to other people, 2) you're trying to answer something that is already known in the literature, etc. Really, what you would need there is friends in the field you want to work in. Unfortunately, you mostly get those by working in academia for long enough to make a reputation and find people you respect. Some people will respond to [well-informed] questions, but it's not the same as working with a mentor in the new field.

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As others have pointed out, the answer to your literal question

Is an engineering PhD enough to publish math stats research?

is

Yes. In fact no degrees are necessary to publish math/stats research.

But I think what you are really asking is

I find myself more interested in mathematics / statistics than engineering. How do I get there from here? In particular, can one become an academic in mathematics and/or statistics with degrees in engineering?

The answer to the second question is shorter: yes, you can. I highly recommend reading a bit about the lives of these two mathematicians. The point is that they got some of their degrees in engineering, but they kept a lively interest in mathematics and in particular had a lot of contact with mathematicians.

So that is the major thing that you should do if you want to segue into mathematics: cultivate strong relationships with the mathematics research community. As others have said, a well-chosen postdoc is ideal for this. Many people nowadays do more than one postdoc. I would recommend that in your case, since you point out that most math PhDs have more mathematical training than you do (which sounds reasonable, by the way), so doing one postdoc where you can spend some time acquiring these mathematical skills may be beneficial.

Let me say finally although you certainly can do whatever you like, I think your chances become much better if you don't simply gradually turn your back on your background and work in engineering but rather positively incorporate it into your mathematical work. Because mathematics (especially highly theoretical mathematics) has such a high "entry fee," even in comparison to other STEM fields, candidates whom a math department can view as "really mathematicians" (or statisticians...) but who have a strongly relevant interest in engineering look like very valuable players. In particular, university deans are all about interdisciplinary stuff nowadays...whereas most pure mathematicians really are not. I think there are a lot of good niches waiting to be occupied; if you can find one, you may have a leg up on some people who were studying only math the whole time.

Thanks for your interest in mathematics (it's pretty great, isn't it?) and good luck.

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Your paper ought to stand by itself. If it is good enough to be published, it will (or at least should) be published.

Of course, people will wonder about your "background." And "engineering" isn't the most usual background for a math paper. Still, it isn't as far out of the way as say, fine arts. And people realize that engineering PhDs have all kinds of "secondary" concentrations. Yours just happens to be math.

If you want "credentials," you might go back to school for a Master's (not necessarily a PhD) in Math or Statistics. But you really don't need to. Your current background (and interest) ought to speak for itself.

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