Due to low karma i can't reply in the relevant comment thread, so I do it here:
Desrtopa wrote:
If you think there's an inconsistency in people's dismissal of UFO eyewitness accounts, I think you may not have grasped the principles of Bayesian reasoning yet.
Baysian reasoning says to treat all evidence equal. The prior may be low, say 0.01, but that's all. There is no weight of the prior that can change. Thus if we see new evidence the update of the probability isn't affected by some magic weight that could diminuize the size of the update arbitrarily much. Agree?
All the 'lowness' of the prior does is to ensure that the posterior doesn't get updated quite as much as it would with a higher prior. I.e. the effect of the prior scales linearly. Agree? Thus, people in this thread saying "eye witness accounts does not count as evidence when it comes to ufos"* can't account for this decision in a Bayesian manner. Agree?
more precisely they are saying: "seeing objects that can't be explained with natural or man made phenomena does not count as evidence for there actually being such objects". This way of thinking has nothing in common with the Bayesian approach. Agree?
You also stated that eye witness accounts of rare things is less reliable than of common things and thus should count less. Is this really so? Isn't a low prior the only mean for the bayesian method to affect the effect of evidence?
If I see a gremlin in plain sight, or rabbit plain as light, Bayesian reasoning wouldn't distinguish between these reports solely on their own account.
The idea that eye witness accounts of rare things is less reliable than eye witness accounts of common things must be grounded in something else than Bayesian reasoning. Perhaps in psychology. Thus I can ask you: do you have a reference to back up your proposition?
Also I can ask you: Do you find your proposition to be in good correspondence with this statement from the Project Blue Book Special Report No. 14: "The higher the quality of the case, the more likely it was to be classified unknown. 35% of the excellent cases were deemed unknowns, as opposed to only 18% of the poorest cases. This was the exact opposite of the result predicted by skeptics, who usually argued unknowns were poorer quality cases involving unreliable witnesses that could be solved if only better information were available." ?
In short: Desrtopa was right and I was wrong: all evidence is not equal.
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?