We don’t know the answer, or even have data for an estimate, and ignorance translates to B = 0.5. Even if you feel you do have justification for saying e.g. B = 0.2 or 0.8 (I did say might in the original), B will have a much less extreme value than F.
edit: Of all the comments I’ve made on LW that I expected to get down voted, this wasn’t one of them. Can the down voters explain your reasons for disagreement?
edit 2: To clarify, I’m not claiming we have no data bearing on the question of whether there is life on Mars—of course we have. I’m claiming different chunks of data support different conclusions, nothing is anywhere near being conclusive, and after all of it is added up, the only reasonable and impartial conclusion at this time is “I don’t know”, for B somewhere in the neighborhood of 0.5.
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.
Good example. I assign B = 0.5 in all three cases, but I expect the (unknown) value of F to be very similar (and close to 0 or 1) for all three, unlike in the case of three coin flips.
The above probability assessments are only coherent if you judge that proposition 1 has the same truth value as proposition 2; I don’t know how that could be justified.
I might bet on B or C against A or D at odds of epsilon to 1, to be settled when we have thoroughly explored Mars, assuming that if there is life, we will find it. This of course depends on the actual value of epsilon.
Put it this way: Of all the things that might have turned out to be controversial, I’m just surprised “we have no idea whether there is life on Mars” turned out to be the one; it still strikes me as fairly obviously reasonable. Oh well, surprises are part of the point of talking to people :-)
The problem may be that “we have no idea whether there is life on Mars” sounds a lot like “we have no evidence about the presence of life on Mars”, which is simply not the case. (Of course, “we have no idea whether there is life on Mars” was operationalized as a probability assessment of 0.5, which does not imply zero evidence, so I can’t be sure if my re-quotation is what you meant.)
Ah, indeed the paraphrased version would be incorrect, and wasn’t what I meant; perhaps I phrased my version badly. I’ve added a clarification to my earlier comment, does that help?
We don’t know the answer, or even have data for an estimate, and ignorance translates to B = 0.5. Even if you feel you do have justification for saying e.g. B = 0.2 or 0.8 (I did say might in the original), B will have a much less extreme value than F.
edit: Of all the comments I’ve made on LW that I expected to get down voted, this wasn’t one of them. Can the down voters explain your reasons for disagreement?
edit 2: To clarify, I’m not claiming we have no data bearing on the question of whether there is life on Mars—of course we have. I’m claiming different chunks of data support different conclusions, nothing is anywhere near being conclusive, and after all of it is added up, the only reasonable and impartial conclusion at this time is “I don’t know”, for B somewhere in the neighborhood of 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.
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.
What probabilities do you assign to the following propositions?
There is life on the northern hemisphere of Mars.
There is life on the southern hemisphere of Mars.
There is life on Mars.
Good example. I assign B = 0.5 in all three cases, but I expect the (unknown) value of F to be very similar (and close to 0 or 1) for all three, unlike in the case of three coin flips.
The above probability assessments are only coherent if you judge that proposition 1 has the same truth value as proposition 2; I don’t know how that could be justified.
Now, without using probabilities of 0 or 1, can you coherently assign probabilities to
Sure. B(A) = B(D) = 0.5, B(B) = B(C) = epsilon. (The 0.5 is only good to one significant figure, and even that’s a stretch.)
Just how small is this epsilon? I might want to propose a bet.
If I had a number, I would’ve given the number instead of saying “epsilon” :) What’s your proposed bet?
I might bet on B or C against A or D at odds of epsilon to 1, to be settled when we have thoroughly explored Mars, assuming that if there is life, we will find it. This of course depends on the actual value of epsilon.
So basically you’re saying that the probability of there being life on only one of the hemispheres is arbitrarily small?
Mathematically nonzero, but small enough that we can treat it as zero for practical purposes, yes.
Can you link to some of the major chunks of data supporting life on Mars?
Even if ignorance were total, some kind of Occam’s-Razor prior would be applicable.
Put it this way: Of all the things that might have turned out to be controversial, I’m just surprised “we have no idea whether there is life on Mars” turned out to be the one; it still strikes me as fairly obviously reasonable. Oh well, surprises are part of the point of talking to people :-)
The problem may be that “we have no idea whether there is life on Mars” sounds a lot like “we have no evidence about the presence of life on Mars”, which is simply not the case. (Of course, “we have no idea whether there is life on Mars” was operationalized as a probability assessment of 0.5, which does not imply zero evidence, so I can’t be sure if my re-quotation is what you meant.)
Ah, indeed the paraphrased version would be incorrect, and wasn’t what I meant; perhaps I phrased my version badly. I’ve added a clarification to my earlier comment, does that help?
Yup.
Surely we have some data.
Right? I’ve seen lots of pictures of Mars and not identified any life in any of them!