Wait, what? Bayesians never assign 0 probability to anything, because it means the probability will always remain 0 regardless of future updates. And "prior probability", by definition, means that we throw out all previous evidence.
Wait, what? Bayesians never assign 0 probability to anything, because it means the probability will always remain 0 regardless of future updates.
Yes. This name for this is Cromwell's rule.
And "prior probability", by definition, means that we throw out all previous evidence.
Not quite. The prior probability is the probability of the hypothesis and the background information, independent from the evidence we are updating on. This includes previous evidence. We usually write the "prior probability" as P(H), but it should really be wr...
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?