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TylerJay comments on Self-Study Questions Thread - Less Wrong Discussion
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"Probability theory" is an extremely broad term. You don't need any calculus to understand discrete random variables (and if your motivation is directed towards MIRI research, this is mostly the kind of probability that's relevant). You'll want to know some one-variable calculus to understand continuous random variables (so you can manipulate probability density functions and maybe characteristic functions). It would be helpful to be comfortable with some multivariable integral calculus for the purpose of understanding collections of continuous random variables, but something like Stokes' theorem won't be particularly relevant.
My impression is that most traditional statistics courses are very bad (not even because of anything to do with frequentism, they're just very bad). Don't take one.
Can you clarify what you mean by this?
Thanks, that's really helpful.
For #3, I was basically looking for some feedback on this text. It was recommended in the best textbooks on every subject thread, but I've heard mixed reviews about it. The top rated review on amazon claims
and another review by a Comp Sci professor calls it "Magisterial, and Impenetrable".
These are not things you see written about something like Sedgewick's book. Interestingly enough, the reviews on this one all similarly praise Sedgewick's book over Cormen.
So I guess my question was "Is Cormen et al. actually a good introductory text on algorithms for someone who has not taken an algorithms course before?"
The answer is "probably not". Cormen is too comprehensive and dry for self-study; it's best used as the textbook to back an algorithms course or as a reference to consult later on.
A very good book is Skiena, The Algorithm Design Manual. I usually recommend it to people who want to brush up on their algorithms before programming interviews, but I think it's accessible enough to a novice as well. Its strengths are an intelligent selection of topics and an emphasis on teaching how to select an algorithm in a real-life situation.
Ah, sorry, I was referring to your question about Jaynes (that question was meant to be numbered with a 4). What are you looking to get out of an introductory probability textbook?
How much of a mathematician are you? I would recommend Cormen et al on its own only to people with a strong mathematical background and plenty of talent. I like the idea of Cormen et al + Skiena together (and I'm pretty sure I said so in that thread) but don't have actual evidence on how well that works in practice.
That's my impression as well. I've had to take a statistics course, and I wound up memorizing procedures enough to vomit it up on tests on homework. There wasn't really a coherent framework, so the least work method of passing the course was memorizing the teacher's passwords.
If you have to take a traditional statistics course, don't expect to get a solid understanding of statistics out of it. Perhaps you'll know how to use certain orthodox analysis methods.
Traditional statistics classes teach procedures, but not the math needed to understand them. Being told to use maths without being told how the maths work is infuriating to certain sorts of people, and those sorts of people are abnormally concentrated on LessWrong. Jaynes builds up procedures from first principles, which appeals to some but is pointlessly abstract for others.
Different minds learn differently. The answer to this poll entirely depends on who you are.
It is worth pointing out that probability and statistics are generally considered to be separate, although closely related topics. Because statistics is built on probability, you are probably better off learning probability first, and then statistics.