What math/stats knowledge does learning Bayesian probability require? I study undergraduate "pure" math and philosophy. I know that a number of philosophers use Bayesian probability to augment their epistemic logic. My school teaches Bayesian probability as a brief part of a fourth year class. Enrolling in it requires completing a series of stats classes that are outside of my path. However, for a few reasons, I suspect that those prerequisites exist to prepare students to learn the other elements of the class that includes the lessons on BP, and that learning BP doesn't require a three year trek through non-Bayesian probability theory. That said, I really don't know. Perhaps I'm wrong.
What math/stats knowledge does learning Bayesian probability require?
 A: You need working knowledge of calculus, like being able to take integrals, and not like knowing Weierstrass theorem. For instance, if you can take this integral without looking at any references with a pen and a paper, you're probably equipped to take the course:
$\int_{-\infty}^{\infty}\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}|x^3|dx$
Knowing linear algebra helps too, but you can pick it up on the way. I'm not talking about anything crazy, it's simple matrix manipulations, pretty much within what's described in Algebra.B section of Madelung's Die Mathematischen Hilfsmittel des Physikers book. It's available online here, and is an awesome little book on applied math. For instance, if you can solve this equation, you're good to go:
$\det\left|\begin{matrix}1-\lambda& 2\\2 &1-\lambda\end{matrix}\right|=0$
You don't need measure theory and real analysis, but it helps to know them. The key is not to enroll in courses taught at math dept for math majors. Take a course specifically designed for applied folks, maybe for psychologists or other math-challenged constituents. Courses taught for physicists could be a good compromise: they have enough math to actually gain useful skills, but they don't bother with proofs and other crazy stuff mathematicians are obsessed about.
A: I was in a similar boat, having been a Math/CS double major but needing to learn a lot of Bayesian probability for work. What I'd recommend:


*

*Practical ability to do and understand integrals

*An understanding of numerical methods for approximating integrals (sampling, Monte Carlo method)

*Knowing the R programming language is very useful - most texts I've come across do the examples in R.

*General understanding of model evaluation - you would certainly get this in stats, but you can get it in other fields (psychology, biology, machine learning) as well.

*There are lots of general modeling "tricks" that I didn't see studying pure math that would have been nice to know before jumping into Bayesian probability, such as regularization and parameter selection.
Since you are a math major, you probably will see real analysis anyway, but I did not really find it that helpful for this. I did not find my background in measure theory helpful either. It very well might be that the class offered at your school is built with the assumed stats background - in which case, I recommend getting a book about Bayesian statistics/probability (I found this one useful) and working through it yourself.
