I received the following email:

My academic background is in international relations and I’ve taken a lot of math as well. I’m considering graduate study in (Bayesian) statistics and would like to do the type of research that you and Prof Jeff Gill (at Washington U) do. I have a couple of quick questions and would appreciate it very much if I could get your comments on these.

1. Does my background sound adequate to you for graduate study in statistics? How far would I be able to go with the background I have?

2. Beyond multivariate calculus, differential equations, and linear algebra (Gilbert Strang’s book), I’ve done all of Rudin’s undergrad analysis text. I’m decent with proofs but not very comfortable with vector calculus (the line/surface integrals stuff). Is that a major handicap? What should I be focusing on to increase my chances of getting into a top program?

My reply: What background is necessary depends on the program. Some stat programs are highly mathematical, others such as University of Washington’s are more diverse, with some students focusing much more on computation or social science than on mathematics. In answer to your second question, I’ve occasionally done some Fourier analysis and I often compute derivatives and integrals, but I don’t think I’ve ever done line or surface integrals.

Really, you need to know mathematics well enough to understand the mathematical expressions that get used in statistical models. For example, if you look at (1/(sqrt(2pi)sigma)exp(-(1/2)(y-mu)/sigma^2), you should be able to quickly understand what sort of function this is, as a function of y, or as a function of mu, or as a function of sigma. All that path integral stuff is more just a way to give you experience so you can do what you need to do.