ChristianKl comments on What Bayesianism taught me - Less Wrong
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Anecdotal evidence is filtered evidence. People often cite the anecdote that supports their belief, while not remembering or not mentioning events that contradict them. You can find people saying anecdotes on any side of a debate, and I see no reason the people who are right would cite anecdotes more.
Of course, if you witness an anecdote with your own eyes, that is not filtered, and you should adjust your beliefs accordingly.
I think the value of anecdotes often doesn't lie so much in changing probabilities of belief but in illustrating what a belief actually is about.
That, and existence/possibility proofs, and, in the very early phases of investigation, providing a direction for inquiry.