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Jack comments on Open Thread: May 2010 - Less Wrong
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I want to understand Bayesian reasoning in detail, in the sense that, I want to take up a statement that is relevant to our daily life and then try to find exactly how much should I believe in it based on the the beliefs that I already have. I think this might be a good exercise for the LW community? If yes, then let's take up a statement, for example, "The whole world is going to be nuked before 2020." And now, based on whatever you know right now, you should form some percentage of belief in this statement. Can someone please show me exactly how to do that?
Well to begin with we need a prior. You can choose one of two wagers. In the first, 1,000,000 blue marble and one red marble are put in a bag. You get to remove one marble, if it is the red one you win a million dollars. Blue you get nothing. In the second wager, you win a million dollars if a a nuclear weapon is detonated under non-testing and non-accidental conditions before 2020. Otherwise, nothing. In both cases you don't get the money until January 1st 2021. Which wager do you prefer?
If you prefer the nuke bet, repeat with 100,000 blue marbles, if you prefer the marbles try 100,000,000. Repeat until you get wagers that are approximately equal in their estimated value to you.
Edit: Commenters other than vinayak should do this too so that he has someone to exchange information with. I think I stop at maybe 200:1 against nuking.
So 200:1 is your prior? Then where's the rest of the calculation? Also, how exactly did you come up with the prior? How did you decide that 200:1 is the right place to stop? Or in other words, can you claim that if a completely rational agent had the same information that you have right now, then that agent would also come up with a prior of 200:1? What you have described is just a way of measuring how much you believe in something. But what I am asking is how do you decide how strong your belief should be.
It's just the numerical expression of how likely I feel a nuclear attack is. (ETA: I didn't just pick it out of thin air. I can give reasons but they aren't mathematically exact. But we could work up to that by considering information about geopolitics, proliferation etc.)
No, I absolutely can't claim that.
By making a lot of predictions and hopefully getting good at it while paying attention to known biases and discussing the proposition with others to catch your errors and gather new information. If you were hoping there was a perfect method for relating information about extremely complex propositions to their probabilities... I don't have that. If anyone here does please share. I have missed this!
But theoretically, if we're even a little bit rational the more updating we do the closer we should get to the the right answer (though I'm not actually sure we're even this rational). So we pick priors and go from there.