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One professor at our institute gave all his students the same advice when it comes to Ph.D. application: apply to non-obvious programs at top universities. Here "obvious programs" refer to the program that aligns well with your area of study. For example, if you are a Master's student in Statistics, then Ph.D. programs in Statistics, Applied Math, or Computer Science are obvious choices, whereas those in Applied Psychology, Electrical Engineering, and Mechanical Engineering are the non-obvious programs he suggests applying to.

His rationale is that the title of a top school helps a lot in job hunting (particularly in the industry), so you should try to get into a school with good prestige. However, obvious programs in these schools will be very competitive with strong applicants having the same background as you, so you should apply to less popular programs instead. He believes the mismatch in area of study is not going to be an issue, because Ph.D. students from every department do applied math in their research, so our quantitive skills will be useful no matter where we go.

I wonder how far should I take this advice. In fact, I do have some interest in electrical engineering, but some schools only allow one application, so I can apply to one program only. On the one hand, I always find hardware accelerators very cool and own a few FPGAs as a hobbyist. In fact, I taught myself Verilog in my gap year (it was the pandemic), which is quite unusual for someone with a Bachelor's in Statistics, so you can tell I do have some passion for EE. Additionally, I have some research experience in deep learning with JAX on TPUs, which means I am at least a user of state-of-the-art hardware accelerators. Moreover, I wrote some CUDA in a course project and am quite good at programming in general, which the recommendation letters can hopefully prove. Finally, for better or worse, my mathematical background makes me a special applicant. On the other hand, I have absolutely zero research experience in EE and few relevant courses on my transcript, as I stopped playing with electronics when I enrolled at a top research university as a Master's student in Statistics: I never consider the option of pursuing a Ph.D. in EE, because I thought it only was for those who have a relevant background.

Is it a good idea for me to apply to EE instead of Statistics? If this question is too narrow for this site, can someone possibly convince the admission committee in the EE department that he/she will be a good Ph.D. candidate with little relevant research experience?

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    What is ‘obvious’ to one person is not obvious to another. Not quite sure why a Masters in statistics is an asset to a PhD Electrical Engineering program compared to a Masters in EE.
    – Jon Custer
    Nov 20 at 3:30
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    EE is not non-obvious. It is super/hyper competitive.
    – VitaminE
    Nov 20 at 4:04
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    If you are able to, you should ask your professor for some specific instances where this advice applies (and possibly has worked). I can see the upside in applying to something adjacent to one's area, say Social Work if one has previously studied Psychology. This would, of course, be an instance where fields overlap.
    – pope
    Nov 20 at 4:25
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    I couldn't disagree more with this advice. You should apply to do research in the subject you want to do research in!
    – astronat
    Nov 20 at 16:22
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    Without any more explanation, this advice could be understood several different ways. One way to understand it, particularly true with your applied math example, is that you might find a PhD program where your background is useful, even if the PhD program depends from a university department that doesn't sound related to your background. Applied math in particular, is useful in most areas of science, so you could find a PhD program in a biology lab or in a physics lab that's suited for an applied math major.
    – Stef
    Nov 21 at 9:05

9 Answers 9

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Probably, what your prof means is the following: find a discipline in which your skill is unique or not common, and critically, it adds value to the discipline. To give you an example, I know of an electrical engineer student who took up a fellowship with a very well-known group in cognitive science. There was a task that the group carried out manually and took days to complete. The student instead wrote a Matlab program and solved it in a few minutes. The researchers in the cognitive science group thought this student is a godsent. On the other hand, in electrical engineering, such a task is equivalent to a third or fourth year lab exercise.

Following the above point, many universities emphasize cross-disciplinary research nowadays and thus have many funding opportunities that require individuals with different expertise. These opportunities may be your door into a top university.

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    I bet the EE student was also very useful in preparing experiments along the lines of "press the button when you hear the beep" or whatever they do in cognitive science.
    – user253751
    Nov 21 at 13:54
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    But, please, for the love of all that is holy, only do this if you actually care about the discipline. If you go into psychology hoping to be able to do applied math without caring for psychology, you will hate it, your advisor will hate it, and you will have nobody to talk to about the things you care about.
    – xLeitix
    Nov 21 at 16:20
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There is probably something valid in the advice, but it would be a mistake to treat that as the top/first level consideration. Much (much) more important is what your career goals are. If you choose a specialty for the doctorate simply because it gets you in the door more easily, but it binds you, at least in the early years, to something you have little interest in, then your long term career goals are harder (much) to meet. There is little worse in life than being trapped in a career path that isn't fulfilling.

After all, your best job opportunities will be in the same field as that of your doctoral study. It will, perhaps, be harder to find a position you would be happy with. Probably not impossible, but you will face the same conundrum - competition.

So, first, decide what your career goals really are. If they have nothing to do with psychology then I'd recommend against joining a psych department just because they use applied math.

If a "non obvious" path is still on the main line to your real objectives, then fine. Otherwise choose a path that is most likely to get you to where you want to go.

Moreover, you might also find a lot of competition for a slot on that non-obvious path, just as much as on the obvious one. But that depends on your academic history and perceived suitability for certain study. In particular if a STEM department is large but a non-STEM department is small, you might find even more competition in the latter.

First, decide on what you really want. The pursue it relentlessly.

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"Ph.D. students from every department do applied math in their research" plus "Applied Psychology" does not compute. (FWIW, I did my Ph.D. in applied math and have coauthored about 20 papers in psychology with Ph.D. students of my psych prof wife.)

Suppose you came out of an applied math or statistics undergrad and did a Ph.D. in psychology, but wanted to stay in math or stats. (If you wanted to switch tracks into psychology, then presumably you would not be posting your question.) When after your psychology Ph.D. you start applying to math/stats jobs, then your employer may well be impressed by your school. But they will also have some very probing question about just why you followed this strange career path. "It was less competitive" will probably not be an answer they will like to hear.

Also, even the "non-obvious" Ph.D. programs at top schools are competitive. Yes, even the tiny little programs, simply because some people want to do a Ph.D. even in Caucasology, and there are simply very few spots that these few people strive mightily for.

Bottom line: I don't think this is very good advice.

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    My concerns exactly. When we hire in field A we will consider applicants from closely related field B, but we view those folks with skepticism. Moreover, in my experience, most of the time they don't actually have the practical experience in field A to do anything in our department but teach intro level courses. They definitely would not meet our tenure criteria of "publish in good quality venues in field A."
    – David
    Nov 21 at 3:07
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If you replace "apply" with "consider" then this is probably good advice, if for no other reason that to help open yourself to wider possibilities and thinking outside the box a little bit.

At the same time, though, I would also urge you to consider two very specific questions:

First, if you are passionate about Subject X (enough so that it is the topic of your Masters degree, and the natural/obvious topic of your PhD) do you really want to spend another four-ish years, minimum, immersed in a detailed study of Subject Y?

Maybe you do! Some people change focus at some point in their career, some have interests so broad as to support this. The answer is not automatically "No." But it's not automatically "Yes," either. It is a question to consider carefully, and if the only reason you are doing this is a tiny degree of competitive advantage, I would consider it very carefully.

Second, PhD programs generally come with breadth requirements. For each non-obvious program you consider applying to, you simply must look over that program's breadth requirements and schedule for completing them to determine if they are realistic. They might simply not be. Jumping from stats to electrical engineering (or vice-versa) is not impossible. But those breadth requirements, especially qualifying exams, are going to be ferocious.

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I had thought of this when entering grad school. I had an undergrad in EE and there were all sorts of options including statistics or even forestry (e.g., tracking mammals with sensors). I was specifically interested in signal processing, and the potential applications are almost endless.

In the end, I applied in EE and got a master's and PhD. I was very interested in the mathematics of waveforms but in my own master's and PhD work there very little use of waveforms and their math, but lots of linear algebra, statistics, and related work with algorithms. I am now a software engineer.

So I went to an 'obvious' programs, but there are several sub-fields of electrical engineering, so even in that choice one has to be discerning.

One caution: It is somewhat hard to pass the written qualifiers in a technical program, and if you did not get an undergrad degree in this program, it would be very difficult to pass the qualifiers. There is certainly EE work that uses statistics, but if one came to the qualifiers with only a statistics background it would require an enormous amount of preparation to actually pass.

I am in the USA and my PhD was obtained in the 1990's, so some things have changed, but I think the basics of understanding the undergrad material needed to pass the qualifiers has not changed.

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His rationale is that the title of a top school helps a lot in job hunting (particularly in the industry), so you should try to get into a school with good prestige.

I agree with this to a point. It is true that, all things being equal, a higher prestige school will be better for your CV than a lower prestige school. However, more important is your passion and research output. You can only be passionate and have enough drive to complete research if you study a topic that you are truly interested in. Going to a prestigious school and then accomplishing nothing because you are depressed about how much time you are spending on topics you didn't want to study in the first place will not lead to better job opportunities later.

So, the most important thing is finding a place where you can study what you are passionate in and be successful. Prestige is a secondary consideration. It's not a bad idea to apply to a "non-obvious" program if you are genuinely interested in making a career in the topic of that other program, but only with the context that this consideration is much less important than doing something you love.

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I see a logical disconnect in the advice. In your example, if you have a Masters degree in statistics, then electrical engineering is a non-obvious choice for a PhD. That part is true, these two degrees are related but not the most straight-forward fit.

But then the conclusion appears to be that electrical engineering is easier to get into than statistics. That would be true only if electrical engineering is a non-obvious choice for PhDs in general, for the population of all candidates regardless of their Masters which at least for this example is definitely wrong.

So if you want to use this advice I think you need to start from the opposite direction. First identify PhD programs that are non-obvious in general and therefore might be somewhat easier to get into. Then check whether the Masters degree you have is at least somewhat of a fit for these programs and if that is the case it might be easier to get into these programs than into a popular PhD program.

The caveat spelled out in other answers that you should only apply to PhD programs you are genuinly interested in of course still applies. Getting into a PhD program you don't actually want is a huge waste for all involved, please don't do that.

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I have some personal experience which you may find relevant. I switched fields at each stage of my academic career. I have a Bachelor's in Physics, a Master's in Environmental Engineering, and a Ph.D. in Biology. I originally applied for several Ph.D. positions which were much more closely related to my Master's degree research, but did not even get called for an interview for the first few. (I don't know what country you are based in, Ph.D. admissions processes vary. I was applying to programs in Sweden, where most Ph.D. students are hired to work on a specific research project.) I saw the position in biology advertised and thought I was unlikely to get it given my background. However, the research project sounded very interesting, and was related to an existing hobby of mine, so I applied for it too, and it is the one I got.

I later had a conversation with my Ph.D. supervisor about why he selected me given that there were many other candidates for my position who had done their master's degree in Biology. He said it was because I seemed genuinely interested in the project, I had skills which would be relevant, I seemed like a strong student, and that anyway the research experience of a master's degree is equivalent to only the first 6 months of a PhD. I have found that skills I picked up in my earlier fields (among them programming and statistics) have been very helpful to me in biology, in part because they are more rare among biology students.

I think your professor's advice is good, if you take it as "you don't have to apply to just a statistics or applied math program, you should think more broadly because your skills will be useful in other fields too." As other answers have said though, you should not apply to a program in a new field just because you think it will be easier to get (although in my case it seems to have been true!). Only enter a Ph.D. program if you actually want to work in that field!

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Such cross-disciplinary curriculum is a tradeoff: you broaden your potential research or employment opportunities, at the expense of expertise. It may be a good idea if you don't know which field of study you prefer, but not so much if you already have a clear preference.

For instance, if you're a Computer Science graduate with a Ph.D. in Mechanical Engineering, you'll be able to apply to both programming and mechanical design positions in industry. However, you will be seen as an inferior candidate for a programming job compared to someone who has a CS masters degree and a Ph.D. in CS, or even to someone with a CS masters degree and 3-5 years of experience (which they got while you were busy with your Ph.D. degree).

The fact that both CS and ME require math will not matter much. In CS you'll probably learn queues and graphs, while in ME you'll concentrate on tensors and the like. There will be some overlap, sure, but don't overestimate it.

The value of a top school degree depends a lot on the country. In some places a the fact that your degree comes from a top-rated school or university will matter more than whether you studied CS or ME. Unfortunately, such top schools tend not to have "non-obvious programs" with less competitive admission criteria, getting into an ME program in such school will likely be as hard as getting into CS.

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