I think you may be confused by an oversimplification of Occam's Razor: "Extraordinary claims require extraordinary evidence." That's not actually how you derive a prior - the very word "extraordinary" implies that you already have experience about what is ordinary and what isn't. If we really throw out all evidence that could tell us how likely aliens are, we end up with a probability which (by the usual method of generating priors), depends on the information-theoretic complexity of the statement "There are aliens on earth." Which in turn depends on how precisely you define the word "aliens". Aliens that fly around in saucers are more likely than aliens that fly around in saucers and want to probe our butts. And aliens that fly around in saucers and probe our butts are more likely than aliens that fly around in saucers and probe our butts and are abducting our politicians one by one to replace them with reptilian impersonators. Every extra caveat makes a statement less likely. Every extra belief you take on is one more way that you could be wrong. This is why you need to justify all your beliefs.
I don't think that generic aliens should be considered especially improbable a priori - before the evidence is considered. I think that they are unlikely a posteriori - based on the fact that we don't see them. I think that any intelligent space-faring life would be busy building spheres around stars (if not outright disassembling the stars) as quickly as they spread out into the cosmos. So we'd notice them by the wake of solar systems going dark. At the very least, there's no reason to think that they would hide from us, which is what these scenarios tend to require (though I haven't watched the documentary).
I'm not sure what you're trying to say about the black swan. What a bayesian would do is assign a prior probability distribution over possible colorations of swans (say 1/2 white, 1/2 black), then calculate, based on the fact that ey has seen, say, a million white swans in a row, what the probability is that the next swan ey sees will be black. Needless to say, ey will be very surprised if the next swan actually is black. But this is a good thing, because, for the same reason, ey was very unsurprised by the previous swan, which was white, as well as swans number 999,999 and 999,998 and 999,997 and so on.
Anyway, I found this amusing.
"I don't think that generic aliens should be considered especially improbable a priori - before the evidence is considered. I think that they are unlikely a posteriori - based on the fact that we don't see them"
Citation?
There's plenty of evidence for non-man made, non-hoaxed, non-astronomical, non-weatherrealated unidentified flying objects according to studies made by the US and French military:
http://en.wikipedia.org/wiki/Project_Blue_Book#Project_Blue_Book_Special_Report_No._14
most important highlights:
Recently I've been struck with a belief in Aliens being present on this Earth. It happened after I watched this documenary (and subsequently several others). My feeling of belief is not particular interesting in itself - I could be lunatic or otherwise psychological dysfunctional. What I'm interested in knowing is to what extend other people, who consider themselves rationalists, feel belief in the existence of aliens on this earth, after watching this documentary. Is anyone willing to try and watch it and then report back?
Another question arising in this matter is how to treat evidence of extraordinary things. Should one require 'extraordinary evidence for extraordinary claims'? I somehow feel that this notion is misguided - it discriminates evidence prior to observation. That is not the right time to start discriminating. At most we should ascribe a prior probability of zero and then do some Bayesian updating to get a posterior. Hmm, if no one has seen a black swan and some bayesian thinking person then sees a black swan a) in the distance or b) up front, what will his a posterior probability of the existence of black swans then be?