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?

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#### Best Answer

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:

$int_{-infty}^{infty}frac{1}{sqrt{2pi}}e^{-frac{x^2}{2}}|x^3|dx$

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:

$detleft|begin{matrix}1-lambda& 2\2 &1-lambdaend{matrix}right|=0$

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.

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