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roundsquare comments on Open Thread June 2010, Part 2 - Less Wrong
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A question about Bayesian reasoning:
I think one of the things that confused me the most about this is that Bayesian reasoning talks about probabilities. When I start with Pr(My Mom Is On The Phone) = 1/6, its very different from saying Pr(I roll a one on a fair die) = 1/6.
In the first case, my mom is either on the phone or not, but I'm just saying that I'm pretty sure she isn't. In the second, something may or may not happen, but its unlikely to happen.
Am I making any sense... or are they really the same thing and I'm over complicating?
Remember, probabilities are not inherent facts of the universe, they are statements about how much you know. You don't have perfect knowledge of the universe, so when I ask, "Is your mum on the phone?" you don't have the guaranteed correct answer ready to go. You don't know with complete certainty.
But you do have some knowledge of the universe, gained through your earlier observations of seeing your mother on the phone occasionally. So rather than just saying "I have absolutely no idea in the slightest", you are able to say something more useful: "It's possible, but unlikely." Probabilities are simply a way to quantify and make precise our imperfect knowledge, so we can form more accurate expectations of the future, and they allow us to manage and update our beliefs in a more refined way through Bayes' Law.
The cases are different in the way that you describe, but the maths of the probability is the same in each case. If you have an unseen die under a cup, and a die that you are about to roll, then one is already determined and the other isn't, but you'd bet at the same odds for each one to come up a six.
I think the difference is that one event is a statement about the present which is either presently true or not, and the other is a prediction. So you could illustrate the difference by using the following pairs: P(Mom on phone now) vs. P(Mom on phone tomorrow at 12:00am). In the dice case P(die just rolled but not yet examined is 1) vs. P(die I will roll will come out 1).
I do agree with Oscar though, the maths should be the same.
You might be interested in this recent discussion, if you haven't seen it already:
http://lesswrong.com/lw/2ax/open_thread_june_2010/23fa
It looks to me like your confusion with these examples just stems from the fact that one event is in the present and the other in the future. Are you still confused if you make it P(Mom will be on the phone at 4 PM tomorrow)= 1/6. Or conversely, you make it P(I rolled a one on the fair die that is now beneath this cup) =1/6
In my experience, when people say something like that it's usually a matter of epistemic vs ontological perspective; and contrasting Laplace's Demon with real-world agents of bounded computational power resolves the difficulty. But that could be overkill
In the second case, you either roll one on the die or not, but you are pretty sure that it will be another number.