I'm going back to school. Again. This time for an MS in Mathematics and Statistics at SIUE.
People ask why. I already have a CS master's. The answer is simple: I kept hitting walls.
The Walls
My CS degree gave me tools. I can implement algorithms. But in my research I kept running into questions I couldn't answer:
- Why does maximum likelihood estimation actually work?
- What are the asymptotic properties of bootstrap confidence intervals?
- How do you prove an estimator is consistent?
I could use these methods. I couldn't derive them. That gap bothered me for years.
What I Want
Rigorous statistical theory. Measure-theoretic probability, asymptotic theory, decision theory. I want to prove theorems, not just run computations. I want to build estimators from first principles and understand why they behave the way they do.
My specific research interest is survival analysis: reliability theory with censored and masked failure data. Components fail, you don't always know which one, and the data is incomplete. That's the problem space.
A Different Mode of Thought
Programming is imperative. You tell the machine what to do, step by step. Mathematics is declarative. You describe what must be true and then prove it.
I've spent most of my life in the imperative mode. I want the declarative mode available to me too. Not as a replacement, but as a complement. The ability to move between formal proof and working implementation is something I don't have yet, and I want it.
What's Next
For the next couple of years: probability theory, statistical inference, linear models, survival analysis, computational statistics.
This will change how I think about problems. That's the point.