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I have a PhD in applied mathematics from a top university. I didn't realise it at the time because I was so focussed on my research, but it seems my research area (numerical analysis of PDEs) is actually very niche in terms of real-world problems in industry.

All the job listings I see are looking for people with a probability/statistics/machine learning background. There are literally hundreds of listings for these types of jobs for every one job in my area. I am currently a postdoc but I plan to leave academia for industry (probably finance) in the near future.

As the need for people with statistical skills is so clear, I have started considering the possibility of doing a second PhD, this time in a statistical area.

It would have to be part-time as I will be working full-time in industry. However, I currently work 7 days a week and very long hours on research as a postdoc, it is my hobby as much as my job. So when I begin working in industry, which is a standard 40 hour Mon-Fri working week, from my perspective I will have a huge amount of free time, i.e. eveninings and weekends, that I could dedicate to statistical research.

So I have several motivating factors for considering doing a second PhD:

  • Statistical skills are very much in demand and are of far more use in real-world applications than my own niche skillset. I would like to work on important real-world problems and it would be ideal to have a qualification for this.
  • I absolutely love research and having a goal to work towards to motivate me to get really deep into a topic. I will have alot of free time when I move to industry soon, and I would like to dedicate that time to something constructive.
  • I am interested in probability and statistics from a theoretical perspective and I would like to make a contribution to this field. Originally I applied for PhDs in this area, along with applied math PhDs; I went with the math PhD as I was also very interested in that area and it was a great opportunity to work with an excellent supervisor and university.

So a second PhD in a statistical area seems to make alot of sense to me.

Questions:

  • Would any professor even be interested in working with me considering that I already a PhD and that I plan to work on the second PhD during evenings and weekends?
  • If you think there are professors that might be interested, how should I go about approaching them? I would not like to appear unprofessional.
  • I don't need any funding as I will be working full-time. Will this help me in finding a professor for a second PhD or is it largely irrelevant?
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    Why do you want to do a second PhD? There is no advantage of obtaining a second PhD in a related field over simply switching your future research to that field. A second PhD is simply not an efficient use of your time and resources. The natural step, if you want to stay connected to academia, would be a post-doc. It's very common to switch to a slightly different field during one of your post-docs. – Roland Mar 11 '20 at 11:21
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    A PhD certifies you can do research. It is not an efficient way of certifying that you have knowledge of a particular field (that was usually a precondition before entering the program). So a second PhD is not going to help you. What you need is to fill the gaps in your knowledge and get some work experience. Probably the most efficient way to fill the knowledge gap is to join some MOOCs. – Maarten Buis Mar 11 '20 at 11:40
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    So, perform research on evenings and weekends. Nobody is saying you can't do that. All we are saying is that you don't need to do a second dissertation. It's quite unlikely that you'd find an advisor anyway, because they would also see it as a waste of their time. What you should look for is a cooperation. You should read the answer to this question. – Roland Mar 11 '20 at 13:14
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    @SecondPhD - you seem to be of the opinion that you need to go do another PhD if what you are working on isn't quite what you did your first PhD on. I would suggest that most PhDs are doing something fairly different within 5-10 years of their thesis, yet do not feel they need to get another PhD - they learned how to learn new stuff on the fly without courses in the first one. – Jon Custer Mar 11 '20 at 14:11
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    I have realised based on the answers I've received that my math PhD will be viewed as essentially equivalent to a stats/ML PhD in industry so I can see now that there is no need to do a second PhD in this area. – SecondPhD Mar 12 '20 at 8:45
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As most of the comments already say, doing a second PhD is probably not a good use of your time and not very helpful. From an industry perspective you have a math PhD, that means you are very smart and can learn anything, especially any maths very quickly. Learning some statistics or machine learning can be very helpful for an industry career but there is no need to get a formal degree in it. You can state in job applications that you have a math PhD and that you know statistics. Even if the statistics is entirely self taught in the real industry world this is equivalent to a PhD in statistics.

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    This. If I ever saw an applicant who returned to school for a second PhD, especially in such a closely related field, it would seriously devalue both degrees - because even after completing one, the person still seemed incapable of independently teaching themselves something new. That's not a good sign. Going back to training wheels is not a step forward. – J... Mar 11 '20 at 20:30
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    "Learning some statistics or machine learning can be very helpful for an industry career but there is no need to get a formal degree in it." As someone who reviews applicants for data scientists, I have to strongly disagree with this. There is plenty of work that someone without formal training in Stats/ML can do, but there's also some work that just can't be. There are plenty of stats related positions that are open if you don't have formal training, but some that are definitively closed. – Cliff AB Mar 11 '20 at 23:26
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    My Ph.D. was in discrete optimization, I was hired for an industry research position in statistics/time series analysis/forecasting, I have been working in this job for 14 years, and I endorse this message. +1. – Stephan Kolassa Mar 12 '20 at 7:21
  • Ok this puts my mind at rest. I thought I had no chance at these jobs compared to stats/ML people but if you say my PhD will be viewed as essentially equivalent in industry then I should be fine. I was concerned I had pigeonholed myself into a niche area. – SecondPhD Mar 12 '20 at 8:41
  • @CliffAB As someone who has transferred into data science from a physics background I disagree with the statement that some can't be done without formal training. I'm not saying its easy but there are plenty of resources out there to learn if you want to. The OP has shown they can learn independently in a related field, I wouldn't have reason to doubt they can do so without another degree/PhD. I believe the idea that anything is 'closed' without formal training is flawed. – Lio Elbammalf Mar 12 '20 at 14:20
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From your question and comments it seems that there are two distinct issues:

  • Finding a good industry job with your profile: since you mention statistics I assume that you are looking at jobs in the area of data science. There is so much demand in this area that you don't even need a formal diploma, you could just teach yourself and acquire some experience with online material. In case you really want a diploma, what you need is a Master, not a PhD.
  • Keeping doing research because you enjoy it: you don't need to do another PhD in order to keep practicing research as a hobby. Most advisors would be reluctant to take you on anyway if you are not able to work full time on the PhD: they would often see you as a "flight risk", since you don't have any specific funding and no strong reason to finish a (second) PhD. However you could certainly collaborate on some research projects, many academics would appreciate a skilled collaborator that they don't have to pay.
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  • Thanks for this advice, this sound like I a great idea. I will attempt to find an academic with experience in this area so I can collaborate while transitioning into this area. – SecondPhD Mar 12 '20 at 8:43
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I'm a retired Uni academic.

If you are determined to study more (and bravo for that), I would strongly recommend an MSc or an MMath in the subject. If you are short on skills, you will get far more from a good Masters. It will be cheaper, quicker and more intensive. Frankly, you will learn more as well. You've proved you can do research and that's the end of PhD for you. You would slow down your career too much by doing another.

Distance learning is appropriate if you are strapped for time.

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I also have a PhD in numerical analysis of PDEs (I would be interested to know in more detail what you studied).

During my studies I made good friends with a senior statistics professor at the university and I was pretty surprised by the amount of overlap some of the things we were looking at. In particular we had a good conversation about applications of the Proper Orthogonal Decomposition which had applications in my particular studies (reduced basis approximations of high dimensions PDEs) as well as in simplifying complex statistical models.

There is also an obvious huge overlap if you ever worked in the area of stochastic PDEs. I feel like I could have definitely continued a post doctorate with this statistics professor if he had anything available and I actually wanted to. I would suggest doing some background research into what some specific statistics professors have been working on and see if you can tie any of it back into your own studies. I think you'll be surprised.

On a side note, I didn't want to continue in academia and instead became a software developer. If you have some computational experience, which I assume you will having done numerical analysis, then I would also recommend looking into this because it is also in huge demand at the moment and it's really fun. ;)

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  • More properly, you did your PhD research on a certain topic. You were awarded your PhD in some larger field, like Math or Comp Sci. – Scott Seidman Mar 12 '20 at 11:20

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