What areas of mathematical statistics are highly employable? I'm about to finish my honours in statistics, and I really want to do a PhD because I find mathematical statistics extremely interesting. Areas of research I most want to do a PhD in are stochastic processes and time series.
However I also want to pursue a career in the private sector after my PhD. I was wondering what areas of mathematical statistics are most used in the private sector, and in what types of jobs?
Obviously I'm not going to do a PhD just because it's employable, but I feel it's definitely something I need to consider and so would like some advice.
 A: If your interest is in skills that are "marketable," I would say learn about a variety of modeling techniques (GLMs, survival models both continuous and discrete, random forests, boosted trees) with an emphasis on prediction over estimation.  Mathematical statistics can occasionally get too bogged down in estimation under parametric models, trying to answer questions that become irrelevant when the model isn't literally true.  So before delving too deeply into a problem consider whether or not it's still interesting and applicable when the model doesn't hold, because it never will.  You should be able to find many such questions in the field of time series, if that's where one of your interests lies.
Also appreciate that there are challenges involved in the analysis of real world data that a statistics education alone may not prepare you for, so I would consider supplementing your education with the study of topics like relational databases and general computation.  These fields can also be very fascinating and offer a refreshing perspective on data.
Finally, as Matthew Drury already pointed out it's essential to be able to program.  I would work on becoming strong with R and / or Python, and start learning about SQL, which you will encounter inevitably.  A lot of companies still use SAS, but do you really want to work for one?  A compiled language such as C or Java also doesn't hurt, but this isn't really critical.
A: As someone who spent their post-doctoral career in industry, I'd say this.


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*Matthew Drury's response is first rate.  dsaxton's remarks on prediction vs estimation are also good.

*Learn to program using whatever will help you get through grad school with speed. Get good at it. Once you are very fluent in one language, other ones are easy to pick up and you can likely do so at your employer's expense.

*Data bases aren't going to get any smaller, and probably won't get any cleaner. I'd predict that techniques to deal with gigantic, messy/missing data are a decent bet over the next two or three decades.  

A: I'm answering as someone who routinely evaluates and hires data scientists.
As a person transitioning from academic study into a private sector career, you're not going to get hired on the strength of any specific skills you have.  The world of academic study in statistics, and the domain of any given company's set of problems are far too vast to hire on the basis of very precisely defined specific skillsets.
Instead, you are going to get hired because you can demonstrate a general aptitude for precise thinking, a thirst and talent for problem solving, an ability to understand and communicate abstract and complex ideas, and a diverse set of practical and theoretical skills.
So, my advice, and I'm just one guy, do what you love and develop a thirst for problem solving, nuance, and complexity.  Learn a diverse set of skills, and know your fundamentals well (better than your research topic)
Oh, and learn to program.

That makes a lot of sense, thanks a lot for the thoughtful reply. Are there any particular programming languages you'd recommend

Hard question to answer without being opinionated.
My personal opinion is that it doesn't really matter, so learn the one that you like and that motivates you to keep learning.  Learning your first language really well is the big hurdle.  After the first learning another (and another, and another) is much, much easier because you have already dealt with the hard conceptual challenges.
But learn the language well, learn how the language works and why it was designed the way it was.  Write clean code that you are unafraid to return to.  Take writing code as a serious responsibility, not a unfortunate reality.  This makes it both more rewarding, and a real skill you can advertise.
If you still want specific advice, I would echo @ssdecontrol, prefer a general purpose language that can do stats over a stats language that can (kinda) do general purpose.
A: Most of the current answers are oriented "data science", which is definitely a highly employable area. As the original poster mentioned a particular interest in stochastic processes and time series, another area of mathematical statistics* that may be relevant is state-space estimation.
This is used to estimate models where the system evolves due to feedback between highly structured (quasi-)deterministic processes and stochastic forcing. For example state-space estimation is ubiquitous in autonomous vehicles.
(*This area is commonly considered to be part of engineering, or other domains, but  certainly involves mathematical statistics.)
A: I wouldn't suggest something radically new, but as a professional data-scavenger myself, I would like to emphasis a few points.


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*All marketable skills are not just only bundle of single isolated skills, but they are a whole synchronized package. And by package, I mean,

*A set of practical skills, with extremely high proficiency. Like you can form meaningful judgement given a pile of data. And for a PhD level guy (or for anyone who is coming to them) the employers would be more interested in bringing real-world cognitive match that you can bring with a given set of data. To clarify, as an example,

*The set of skills that you may employ for data extraction from API, writing codecs and drivers in the process if you've found the process unyielding to the extent where you may not be able engage your full potential to it. Then using elements of the statistical analysis for a transformation of data into information. This process is so raw and so authentic that the more diverse and deep your learning is, the much better information(s), you can retrieve. I have been told once, that the mastering mathematics which can give an answer to the problem is one thing but to interpret that answer in the real world, is just another skill.

*Lastly and extremely important, can you present visualizations of your conclusions for everyone to see and understand without anyone who is not of your related field not asking more than 3 follow-up questions. And this is where you would be giving your analogy to the real-world process(es). It is a bit difficult but once mastered, it usually pays good dividends, throughout your career.
For all these, from my point of view, a useful tip is to ask oneself consistently while studying new things that how it can be employed in the real world. Yes, it does get awkward at times when one delves deep into abstractions but nevertheless it is a habit very well worth it, and often it separates the super-employable from the merely highly educated. Good Luck!
