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.

More to the point, we're never that ignorant.

Sure we are. A priori, the probability that there's something instead of nothing is .5.

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.

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 :-)

Right? I've seen lots of pictures of Mars and not identified any life in any of them!