I never really got the Fermi paradox. There are so many unknowns about "what it takes to reach intelligent life" that I don't think we really can give any estimate - and not seeing any trace of intelligent alien life just should encourage us to consider the "rare earth hypothesis" (that there are some very specific settings regarding Earth, like having a big moon, which are required for intelligent life to evolve, and are very rare in the universe). There are so many things we can forget to consider about Earth (like, the fact it's far from the center of the galaxy, so not exposed frequently to nova) making it special, and so many unknown about the details of evolution of rational life, that it doesn't strike me as impossible that there is in average 1 intelligent life form emerging between 10 billions of years and 15 billions of years after the big bang in a sphere of 5 billions light-years wide, leading to us being alone in our past cone.
...Life arose on Earth sometime in the first few hundred million years after the young planet had cooled to the point that it could support water-based organisms on its surface. The early emergence of life on Earth has been taken as evidence that the probability of abiogenesis is high, if starting from young-Earth-like conditions. We revisit this argument quantitatively in a Bayesian statistical framework. By constructing a simple model of the probability of abiogenesis, we calculate a Bayesian estimate of its posterior probability, given the data that life
Not entirely relevant to the main issues of lesswrong, but possibly still of interest: my talk entitled "von Neumann probes and Dyson spheres: what exploratory engineering can tell us about the Fermi paradox".
Abstract: The Fermi paradox is the contrast between the high estimate of the likelihood of extraterritorial civilizations, and the lack of visible evidence of them. But what sort of evidence should we expect to see? This is what exploratory engineering can tell us, giving us estimates of what kind of cosmic structures are plausibly constructable by advanced civilizations, and what traces they would leave. Based on our current knowledge, it seems that it would be easy for such a civilization to rapidly occupy vast swathes of the universe in a visible fashion. There are game-theoretic reasons to suppose that they would do so. This leads to a worsening of the Fermi paradox, reducing the likelihood of "advanced but unseen" civilizations, even in other galaxies.
The slides from the talk can be found here (thanks, Luke!).