I guess the distinction in my mind is that in a Bayesian approach one enumerates the various hypothesis ahead of time. This is in contrast to coming up with a single hypothesis and then adding in more refined versions based on results. There are trade-offs between the two. Once you get going with a Bayesian approach you are much better protected against bias; however if you are missing some hypothesis from your prior you don't find it.
Here are some specific responses to the 4 answers:
If you have a problem for which it is easy to enumerate the hypotheses, and have statistical data, then Bayes is great. If in addition you have a good prior probability distribution then you have the additional advantage that it is much easier to avoid bias. However if you find you are having to add in new hypotheses as you investigate then I would say you are using a hybrid method.
Even without Bayes one is supposed to specifically look for alternate hypothesis and search for the best answer.
On the Less Wrong welcome page the link next to the Bayesian link is a reference to the 2 4 6 experiment. I'd say this is an example of a problem poorly suited to Bayesian reasoning. It's not a statistical problem, and it's really hard to enumerate the prior for all rules for a list of 3 numbers ordered by simplicity. There's clearly a problem with confirmation bias, but I would say the thing to do is to step back and do some careful experimentation along traditional lines. Maybe Bayesian reasoning is helpful because it would encourage you to do that?
I would agree that a rationalist needs to be exposed to these concepts.
I wonder about this statement the most. It's hard to judge qualitative statements about probabilities. For example, I can say that I had a low prior belief in cryonics, and since reading articles here I have updated and now have a higher probability. I know I had some biases against the idea. However, I still don't agree and it's difficult to tell how much progress I've made in understanding the arguments.
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A list of some posts that are pretty awesome
I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
More suggestions are welcome! Or just check out the top-rated posts from the history of Less Wrong. Most posts at +50 or more are well worth your time.
Welcome to Less Wrong, and we look forward to hearing from you throughout the site!
Note from orthonormal: MBlume and other contributors wrote the original version of this welcome post, and I've edited it a fair bit. If there's anything I should add or update on this post (especially broken links), please send me a private message—I may not notice a comment on the post. Finally, once this gets past 500 comments, anyone is welcome to copy and edit this intro to start the next welcome thread.