As you see more and more heads, you become increasingly convinced the coins are biased. What’s the bias? With what probability p will a given flip come up heads? At the start you assign some mass to p=1, and some to lesser biases. After 10^1000 heads you can basically ignore the possibility that the coins are fair, and most of the weight you might have initially placed on a minor bias. Going from 10^1000 to 3^^^^3 coins, you will get to clobber hypotheses like “p=1-10^2000”, but you will get no evidence whatsoever against “p=1″. So as long as you assigned any non-infinitesimal, non-gerrymandered credence to p=1 at the start, longer sequences can’t get probabilities approaching zero.
True, but that is as you see more heads. You can’t actually update your value for p based on evidence you haven’t seen yet, longer sequences would still have probabilities approaching zero.
Can someone let me know why this has negative votes please? Thanks.
Can someone let me know why this has negative votes please? Thanks.
Because its likes/dislikes not votes. The number of dislikes is greater than number of likes by 1. That being said, as the estimate of bias in coin increases, so does your likehood of future throws being HHHHH. Not sure I understand what is your point.
Hover over the thumbs-up / thumbs-down icons, they say “Vote up” and “Vote down”. Anyway I was wondering what it was that I’d said that was wrong and thus deserved to be voted down.
Yes, I agree. However what I was trying to point out is that if you start off with no evidence of the coin being biased then you estimate of the bias won’t increase before you start flipping coins.
By the same merits, your estimate of how likely it is the mugger will kill x number of people won’t change because every person he kills is evidence toward him killing them all successfully as you’re making the prediction before he does anything. If you read the above comments I believe it makes sense in context.
Hover over the thumbs-up / thumbs-down icons, they say “Vote up” and “Vote down”.
We have a saying in Russian, along the lines of ′ the wall of a shed says [certain swearword common in graffiti, refers to a reproductive organ] but this body part is not present inside the shed ′ . edit: anyhow, i kind of don’t see anything wrong about what you said.
As you see more and more heads, you become increasingly convinced the coins are biased. What’s the bias? With what probability p will a given flip come up heads? At the start you assign some mass to p=1, and some to lesser biases. After 10^1000 heads you can basically ignore the possibility that the coins are fair, and most of the weight you might have initially placed on a minor bias. Going from 10^1000 to 3^^^^3 coins, you will get to clobber hypotheses like “p=1-10^2000”, but you will get no evidence whatsoever against “p=1″. So as long as you assigned any non-infinitesimal, non-gerrymandered credence to p=1 at the start, longer sequences can’t get probabilities approaching zero.
True, but that is as you see more heads. You can’t actually update your value for p based on evidence you haven’t seen yet, longer sequences would still have probabilities approaching zero.
Can someone let me know why this has negative votes please? Thanks.
Because its likes/dislikes not votes. The number of dislikes is greater than number of likes by 1. That being said, as the estimate of bias in coin increases, so does your likehood of future throws being HHHHH. Not sure I understand what is your point.
Hover over the thumbs-up / thumbs-down icons, they say “Vote up” and “Vote down”. Anyway I was wondering what it was that I’d said that was wrong and thus deserved to be voted down.
Yes, I agree. However what I was trying to point out is that if you start off with no evidence of the coin being biased then you estimate of the bias won’t increase before you start flipping coins.
By the same merits, your estimate of how likely it is the mugger will kill x number of people won’t change because every person he kills is evidence toward him killing them all successfully as you’re making the prediction before he does anything. If you read the above comments I believe it makes sense in context.
We have a saying in Russian, along the lines of ′ the wall of a shed says [certain swearword common in graffiti, refers to a reproductive organ] but this body part is not present inside the shed ′ . edit: anyhow, i kind of don’t see anything wrong about what you said.