I was reading the GraphSLAM paper to get a sense of the algorithms used for SLAM purposes in robots. While reading it, I realized that I have a tenuous grasp on probability theory, especially on topics like covariance, conditional probability and multivariate distributions (even things like what posterior probability represents).
I'd like to rectify this and gain an intuitive understanding of the subject, since it is commonly used in numerous areas of engineering.
I dislike books that introduce fully formed theorems with no derivation or proof of how they came into existence. Which comprehensive book(s) can I read?
This book is tough. Really tough. However, you are really going to do "deliberate practice" while having a go on the assignments.
It bothers me that the author does not provide the answer to most of the questions. This is specially bad in this field of Mathematics (Probability). As an example, in calculus you can always plot the curve, the derivative and see if the result makes sense, in probability theory it is hard to have a simple and safe sanity check.
You can watch all classes from Harvard here for free: https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB...
If you want, there is also a MOOC in EdX with the same material: https://www.edx.org/course/introduction-to-probability-0
Sheldon Ross' book is also a good one. It was mentioned here. I specially like the section on theoritical problems, only with exercises on proofs. Every chapter has one. However, Joe Blitzstein problems are more challenging and will train you more on intuition.
It's available for free online, although most people I know end up buying the book[2].
[1] http://www.inference.org.uk/itila/
[2] http://www.inference.org.uk/itprnn/book.pdf
Someone has a great sense of humor :)
Still worth reading, but maybe not a good place to start.
Venkatesh's more recent volume [2] is very well motivated and is better suited to modern engineering applications. Both have lots of exercises.
[1] https://www.amazon.com/Introduction-Probability-Theory-Appli...
[2] https://www.amazon.com/Theory-Probability-Explorations-Appli...
https://www.zabaras.com/courses
I prefer 2017 version