Debating biostatistics vs computational math

[qpoiz]

Hello gradcafe,

I am interested in pursuing a PhD in biostatistics but am concerned that I may not get to work with theoretical math.

Ideally I would like to apply theoretical math in fields like computational neuroscience, AI, cyber security, crypto-currency and I presume that these disciplines are degrees apart from biostatistics. On the other hand, I very much enjoy (big data) analytics, predictive modeling that comes with studying biostatistics.

From you guys' experience, is there a degree/field that has a rigorous curriculum for both biostatistics and pure math? I would most likely take programming/machine learning courses as electives. There is also the (anecdotal) consensus - learning applied math (like stat) is more marketable than learning pure math - that adds to my dilemma.

Should I focus more on degrees like computational science and engineering; computational and applied mathematics and become a fellow of actuarial science (FSA) on the side? Although this teaches statistics, I cannot say how related it will be to biostatistics.

I have a BS in biochemistry so getting the prereqs lined for a PhD in pure math will be much more difficult. I did my post-bac to take calc 1-3 sequence, linear algebra, diff. equation, real analysis, statistics, and combinatorics.

Thank you very much for your time and help.

[localfdr]

I really think that what you mean by pure/theoretical math is what most people call applied math. Also your post is a bit confusing... But my general feeling is that a Statistics department would be a great choice for you! You can do biostat applications in most departments (including neuroscience which is not really traditional biostat), take quite theoretical math classes (measure theory), computational (programming, optimization) and statistical machine learning classes.

[qpoiz]

Thank you, @localfdr. Yes, you are correct that I was using the wrong terminology and could've explained better. Essentially I would like to study what is traditionally known as math in an applied field and also learn statistics. Would you say that pursuing a statistics phd is better than a biostatistics phd for my intentions? Is statistics phd better because most biostatistics do not offer theoretical math courses as elective?

Considering that I am not from a math background and I have a relatively short record of math, how difficult would it be to gain admission into an applied math and statistics phd program?

Thank you again for your input.

[localfdr]

So if I understand it correctly, you want rigorous math, statistics and machine learning (and AI etc), but come from a biological background.

Well actually it really depends on the University. For example, for UW I think you could apply to their biostatistics department, because they also have rigorous math courses and also machine learning (which is what you want I think). In contrast, other biostats programs place a lot more emphasis on computational biology/public health/epidemiology applications rather than on rigorous math (e.g. Harvard biostats), so these would not be a good fit for you.

On the other hand, you will get rigorous math and a good dose of machine learning (if you are interested in that), in pretty much any statistics department, which is why I recommended it. Plus you can always do biological applications in stats departments.

Of course, indeed your mostly biological background means that you will have a better shot at getting admitted at biostats programs. But still, I think you have covered almost all math courses that are important for a stats PhD program and some stats departments look for people with an applied rather than math-y background. Depending on your research experience/GPA/LORs I definitely think you could have a shot at getting admitted to stats programs. Very mathematical programs (usually the ones which also have probability theorists in the stats department, such as Berkeley) might be a longer shot, but maybe still doable with a very strong GRE math subject test.

In conclusion, my advice would be to apply to some biostats departments which are similar to UW plus to a few stats departments.

Edited March 8, 2016 by localfdr

[compscian]

Hi @inbrsuan and @localfdr

I was in a similar situation last year where I applied to computational/applied math PhD programs intending to work on AI, machine learning, and neuroscience. I should tell you at the outset that this is an extremely bad idea! I essentially wasted a year, reapplied, and got into programs that would allow me to pursue the above interests.

Firstly, understand that applied/computational math and AI are very far from each other. This depends to an extent on the university, but the major focus of applied math programs is to develop mathematical tools for analyzing and simulating problems that occur predominantly in natural sciences (Physics, Chem, Bio) and to a lesser extent, engineering. They totally disregard statistics, especially if there is a department called "statistics" in the university. To get a flavor of what most applied math programs offer, have a look at the program of Northwestern university (a top 5 program). It has nothing to do with ML or AI.

Similarly, biostatistics will offer nothing in the vain of AI or ML. It's also hard to market a biostatistics degree for anything other than biostatistics. IMHO, it's overspecializing to such an extent that you will be ineligible for a large chunk of the job market. If it's a real serious AI job, they would naturally hire someone who has specialized in the same, as opposed to someone from biostatistics. The "flavor" offered in statistics is also very different from AI. People in AI study and use statistics to create intelligent agents, whereas people in statistics study the properties of estimators themselves. There is certainly overlap in theory and methods, but the end objective, career trajectories, and "flavor" are very different!

If your interest is in Artificial Intelligence, you should apply to basically CS and EE programs. Only these will allow you to work on intelligent agents and techniques for programming them. A very few select programs like CNS at Caltech are also a possibility. I will stay clear of statistics, biostatistics, and applied math. If your interest is data science, statistics will also work in addition to CS and EE. However, data science and AI are very different, both in terms of final objective and flavor.