Fermi's paradox, extraterrestrial life and the future of humanity: a Bayesian analysis

The Great Filter interpretation of Fermi's great silence asserts that $Npq$ is not a very large number, where $N$ is the number of potentially life-supporting planets in the observable universe, $p$ is the probability that a randomly chosen such planet develops intelligent life to the level of present-day human civilization, and $q$ is the conditional probability that it then goes on to develop a technological supercivilization visible all over the observable universe. Evidence suggests that $N$ is huge, which implies that $pq$ is very small. Hanson (1998) and Bostrom (2008) have argued that the discovery of extraterrestrial life would point towards $p$ not being small and therefore a very small $q$, which can be seen as bad news for humanity's prospects of colonizing the universe. Here we investigate whether a Bayesian analysis supports their argument, and the answer turns out to depend critically on the choice of prior distribution.