> "Bayesian Data Analysis" by Andrew Gelman is another great read.
If you want to read that book you need real analysis more specifically measure theory (unless that subject is in probability theory for you). You cannot get into the last few chapters without it. Dirichlet Process are described using measures.
I don't believe you need multivar calc or info theory. Info theory stuff are used but not as often. I believe you're slanted toward researcher phd position. Gini index, entropy, etc... and such are taken as given when needed.
My recollection is that you need neither real analysis nor measure theory to appreciate it, but it's been a while since I read it. You might get more out of it if you have studied those.
I disagree on multivar calc. Statistics often makes use of matrix derivatives. I have found it helpful to know.
What's required as a prereq to Measure Theory? Any suggestions on good resources for learning Measure Theory?
I have a vague notion that Probability and Measure Theory are intertwined / related somehow, but have never studied the latter specifically.
The relationship is that measure theory provides the theoretical framework for making probability theory rigorous.
The only formal prerequisite for learning measure theory is that you should know series and sequences. For a reference, I'm not so sure, maybe Halmos's book. The important parts are probably:
- Monotone convergence theorem
- Dominated convergence theorem
- The construction of the Lebesgue integral
- Fubini's theorem and Tonelli's theorem
I would probably try not to get bogged down in details of construction of measures (unless you like that) and take the Lebesgue measure (essentially length) as given. Also check out the Radon-Nikodym theorem which states that we can always (ish) work with density functions.
The typical prerequisite for measure theory is a two-semester real analysis course, a la Rudin or any of its alternatives (I particularly like Pugh's book). A solid topological background is also a good idea, although you can probably get away with whatever you learned in real analysis. Two standard measure theory texts are Folland's Real Analysis and the first half of Rudin's Real and Complex Analysis.
Probability theory is the study of distributions of constant measure in measure theoretic terms. There are some good resources that mtzet mentions, but I just wanted to note that a lot of the integration terminology which you take for granted reading about probability theory is formally defined in measure theory. It's also very nice for making signal processing math more formal.
If you want to read that book you need real analysis more specifically measure theory (unless that subject is in probability theory for you). You cannot get into the last few chapters without it. Dirichlet Process are described using measures.
I don't believe you need multivar calc or info theory. Info theory stuff are used but not as often. I believe you're slanted toward researcher phd position. Gini index, entropy, etc... and such are taken as given when needed.