We don’t [...] even have data for an estimate, and ignorance translates to B = 0.5.
(Downvoted.) No, it doesn’t: we know quite a bit about Mars and about life, surely enough to have some sort of prior probability before encountering specific data. More to the point, we’re never that ignorant. If you literally had no information about a topic, then you wouldn’t know enough to even phrase a question about it, or recognize an answer to such a question. By asking the question, you must have some notion in your mind of what you’re asking about, and it is from that notion that we must draw our prior probabilities, rather than arbitrarily picking 0.5. “Whereof we cannot speak, we must pass over in silence.”
So priors matter if you and I have already updated our beliefs on really divergent sets of data. But if you’re coming at a question from a place of total ignorance assigning even possibilities as your priors should work just fine. 0.5 sounds just fine to me. It doesn’t really matter though because as soon as we have any significant amount of evidence to update on our beliefs will rapidly converge. My prior probability for life on Mars could be 99.99, as soon as my rover gets there and doesn’t find any life that number drops dramatically. My prior could also be 0.01 but as soon as I learn about the geological indicators that suggest early Mars was much like early Earth that is going to go up somewhat (and come down again when I show up and don’t see any life) either way the whole point is that it shouldn’t matter much at all what your priors are.
At least that is how it was explained to me, I could be totally off base.
What doesn’t make sense about rwallace’s position is just that he doesn’t seem to think we have any evidence to update on when it comes to life on Mars.
I’m not saying we have no data on Mars. I’m saying we have evidence one person reasonably believes is in favor of life on Mars, and evidence another person reasonably believes is against life on Mars; we even have knowledgeable scientists holding very strong opinions on either side of the issue. My conclusion is that when you add it all up, the net evidence doesn’t justify a position very far from 0.5, and to take a position like 0.01 or 0.99 is really an expression of personal bias.
My conclusion is that when you add it all up, the net evidence doesn’t justify a position very far from 0.5, and to take a position like 0.01 or 0.99 is really an expression of personal bias.
Well thats an interesting conclusion and maybe someone has written something somewhere demonstrating that the right posterior probability given our science is around 0.5. But you can hardly expect your reader to have any idea where that number is coming from. 0.5 sounds much too high to me though what I know I basically know from general scientific knowledge and having done a science report on Mars in the 4th grade.
I agree that 99.99 or 00.01 seem much too extreme for estimations given our evidence- but they’d function perfectly fine as priors, was my point.
(Downvoted.) No, it doesn’t: we know quite a bit about Mars and about life, surely enough to have some sort of prior probability before encountering specific data. More to the point, we’re never that ignorant. If you literally had no information about a topic, then you wouldn’t know enough to even phrase a question about it, or recognize an answer to such a question. By asking the question, you must have some notion in your mind of what you’re asking about, and it is from that notion that we must draw our prior probabilities, rather than arbitrarily picking 0.5. “Whereof we cannot speak, we must pass over in silence.”
So priors matter if you and I have already updated our beliefs on really divergent sets of data. But if you’re coming at a question from a place of total ignorance assigning even possibilities as your priors should work just fine. 0.5 sounds just fine to me. It doesn’t really matter though because as soon as we have any significant amount of evidence to update on our beliefs will rapidly converge. My prior probability for life on Mars could be 99.99, as soon as my rover gets there and doesn’t find any life that number drops dramatically. My prior could also be 0.01 but as soon as I learn about the geological indicators that suggest early Mars was much like early Earth that is going to go up somewhat (and come down again when I show up and don’t see any life) either way the whole point is that it shouldn’t matter much at all what your priors are.
At least that is how it was explained to me, I could be totally off base.
What doesn’t make sense about rwallace’s position is just that he doesn’t seem to think we have any evidence to update on when it comes to life on Mars.
I’m not saying we have no data on Mars. I’m saying we have evidence one person reasonably believes is in favor of life on Mars, and evidence another person reasonably believes is against life on Mars; we even have knowledgeable scientists holding very strong opinions on either side of the issue. My conclusion is that when you add it all up, the net evidence doesn’t justify a position very far from 0.5, and to take a position like 0.01 or 0.99 is really an expression of personal bias.
Well thats an interesting conclusion and maybe someone has written something somewhere demonstrating that the right posterior probability given our science is around 0.5. But you can hardly expect your reader to have any idea where that number is coming from. 0.5 sounds much too high to me though what I know I basically know from general scientific knowledge and having done a science report on Mars in the 4th grade.
I agree that 99.99 or 00.01 seem much too extreme for estimations given our evidence- but they’d function perfectly fine as priors, was my point.
Sure we are. A priori, the probability that there’s something instead of nothing is .5.