/sci/ - Science & Math » Thread #12970315

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Anonymous Tue 13 Apr 19:21:58 2021 No.12970315 View Reply Original Report

Quoted By: >>12970885

Any good resource on statistical probability theory notation and how to simplify/solve such expressions?
Like what the fuck is that notation?
What level of abstraction do I have to work with here. Where do I plug what?

Anonymous

Anonymous Tue 13 Apr 2021 21:13:16 No.12970885 Report

Quoted By: >>12970890

>>12970315
Which parts seem non-standard to you? Is it the Pr(dx,dy) or the conditional expectations? For the former, you can get reasonably far by just interpreting Pr(dx,dy) as an integral over the joint density or sum over the joint probability mass function -- e.g:

$\int [y - f(x)]^2 Pr(dx,dy)<br />= \int [y-f(x)]^2 \varphi_{x,y}(x,y) dx dy$

Where phi is the joint density. Conditional expectation should really be learned on its own. If you've had a first course in probability I'd recommend Grimmett and Stirzaker's probability and random processes if you just want the meat, or Durrett's Probability theory if you want the whole thing with measure theory.

Anonymous

Anonymous Tue 13 Apr 2021 21:15:08 No.12970890 Report

Quoted By:

>>12970885
I guess I should also mention that the reason that notation is used (Pr(dx,dy)) is because modern probability is built on measure theory, which uses different kinds of integrals, hence the different notation.

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