As a simplified example, suppose we have prior reason to suspect that there is a single per-universe parameter p giving an independent per planet chance of technological civilization arising within 10 billion years or so that is log-uniform over [10^-100, 10^-0].
A civilization makes the Fermi observation: that they are not themselves (yet) starfaring and see no evidence of civilizations elsewhere. What update should they make to get a posterior credence distribution for the parameter?
By what criteria should we judge it to be a correct update?
The distribution of number of such civilizations per galaxy doesn’t much depend upon p for values above 10^-11 or so, but drops off quite linearly below that.
Yes, that’s true.
As a simplified example, suppose we have prior reason to suspect that there is a single per-universe parameter p giving an independent per planet chance of technological civilization arising within 10 billion years or so that is log-uniform over [10^-100, 10^-0].
A civilization makes the Fermi observation: that they are not themselves (yet) starfaring and see no evidence of civilizations elsewhere. What update should they make to get a posterior credence distribution for the parameter?
By what criteria should we judge it to be a correct update?
The distribution of number of such civilizations per galaxy doesn’t much depend upon p for values above 10^-11 or so, but drops off quite linearly below that.