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Pardon me, but I'm not sure what you mean by quantity of interest. If the quantity of interest can always be re-cast as a value which is necessarily 1, isn't "q
by ulmus 10y ago
Pardon me, but I'm not sure what you mean by quantity of interest. If the quantity of interest can always be re-cast as a value which is necessarily 1, isn't "quantity of interest" the same for all probability problems?
- lisper 10y agoSorry, I wasn't very clear. > the authors essentially claim to know the probability of their own existence The "quantity of interest" is the probability of aliens, but not the probability of aliens in all possible worlds, but rather the probability of aliens in this world. In this world, the probability that the authors exist is 1.
- ulmus 10y agoI respectfully disagree. I claim the probability of human existence could have been less than 1, just as the probability of heads when tossing a fair coin is less than one, even when heads is observed as an outcome. We simply can't observe "tails" in this case.
- lisper 10y agoYou are confusing two (perhaps three) different things. The probability of a fair coin landing heads is 1/2 before the coin has been flipped. After the coin has been flipped, the probability is either 0 or 1. You may not know which it is, but it is definitely one or the other (assuming classical mechanics). Now, if you are being a strict Bayesian then the probability of the coin being heads is never quite 0 or 1 because there is always the possibility that your eyes are deceiving you, or you are suffering from delusions or some equally unlikely contingency. But I assume that's not what you mean, and that you accept that humans do in fact exist in this universe, in which case the probability that humans exist in this universe is exactly 1. P(A|A)=1 by definition.