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Benito comments on Open Thread, December 2-8, 2013 - Less Wrong
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I've been teaching myself the basics of probability theory (I'm sixteen) but I'm having trouble on the first step. My basic definitions of probabilities are all frequentist, and I don't know a good Bayesian source appropriate for a secondary school student. Is Jaynes' PT:LOS able to be read by moi, given that I know basic set theory? If not, can anyone recommend a different textbook?
Jayne's book probably requires a university undergraduate-level familiarity with probability theory to fully appreciate.
I'd say that for the time being you don't need to worry about bayesianism vs. frequentism. Just learn the basics of probability theory and learn how to solve problems.
Thanks for being the one commenter who told me how tough the book is - I'm leaving it for now, and the below recommendation of 'Understanding Uncertainty' was very useful for understanding what a probability is. After that, I've got some basic probability textbooks waiting to go. Cheers.
It's worth knowing that what Jaynes calls "probability" everyone else calls "statistics."
Generally, "probability theory" means studying well-specified random models. In some sense this is frequentist, but in another sense the distinction does not apply. Whereas "statistics" is about subjective ignorance.
That terminology sounds strange to me.
I define statistics as a toolbox of methods to deal with uncertainty.
And simulation theory is kinda the opposite of statistics - whereas in statistics you deduce the distribution from sample data, in simulation you compute plausible sample data from a given distribution.
If you're looking for an elementary introduction to Bayesian probability theory, I recommend Dennis Lindley's Understanding Uncertainty. A lot more accessible than Jaynes, but not dumbed down. It's informal, but it covers a number of quite sophisticated topics.
Lindley is one of the architects of the Bayesian conspiracy.
This recommendation has helped me out a lot, I might do a write-up of the book as a LW post at some point in the future. Thanks.
Given that PT:LOS is free online you can just try reading it. Even if you don't understand all the maths (do you know some calculus?) you'll still be able to read his verbal explanations of things, which will give you a good idea of the distinction between frequentist statistics and Bayes.
IIRC the version that's online is not the same as the dead-tree version you can buy; the latter has extra material and bugfixes. (I do, none the less, think reading the online version is a good way for Benito to determine whether he finds it approachable.)
Indeed. (Although the dead-tree version doesn't have that much extra material. It mostly just has the "--Much more here!!!--"" notices deleted.)
A good way to find out would be to try reading it.
With math, it's useful to be able to distinguish books you can't understand because you're missing prerequisite knowledge from books you can't understand because you just aren't reading them carefully enough. The prevailing wisdom seems to be that you can't really expect to be able to follow Jaynes through if you pick it up as your first serious textbook on probability.