Bayesian theorem is just one of many mathematical equations, like for example Pythagorean theorem. There is inherently nothing magical about it.
It just happens to explain one problem with the current scientific publishing process: neglecting base rates. Which sometimes seems like this: "I designed an experiment that would prove a false hypothesis only with probability p = 0.05. My experiment has succeeded. Please publish my paper in your journal!"
(I guess I am exaggerating a bit here, but many people 'doing science' would not understand immediately what is wrong with this. And that would be those who even bother to calculate the p-value. Not everyone who is employed as a scientist is necessarily good at math. Many people get paid for doing bad science.)
This kind of thinking has the following problem: Even if you invent hundred completely stupid hypotheses; if you design experiments that would prove a false hypothesis only with p = 0.05, that means five of them would be proved by the experiment. If you show someone else all hundred experiments together, they may understand what is wrong. But you are more likely to send only the successful five ones to the journal, aren't you? -- But how exactly is the journal supposed to react to this? Should they ask: "Did you do many other experiments, even ones completely irrelevant to this specific hypothesis? Because, you know, that somehow undermines the credibility of this one."
The current scientific publishing process has a bias. Bayesian theorem explains it. We care about science, and we care about science being done correctly.
It just happens to explain one problem with the current scientific publishing process: neglecting base rates. Which sometimes seems like this: "I designed an experiment that would prove a false hypothesis only with probability p = 0.05. My experiment has succeeded. Please publish my paper in your journal!"
That's not neglecting base rates, that's called selection bias combined with incentives to publish. Bayes theorem isn't going to help you with this.
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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.