I would instead look at the various steps in the filter, and generalize the parameters of those steps, which then generate universes with various levels of noise / age at first space-colonizing civilization. If you have fat-tailed priors on those parameters, I think you’ll get that it’s more likely for there to be one dominant factor in the filter. Maybe I should take the effort to formalize that argument.
Another way of thinking about the filter/steps is as a continuous developmental trajectory. We have a reasonable good idea of one sample trajectory—the history of our solar system—and we want to determine if this particular civilization-bearing subspace we are in is like the main sequence or more like a tightrope.
If the development stages have lots of conjuctive/multiplicative dependencies (for example: early life requires a terrestrial planet in the habitable zone with the right settings for various parameters), then a lognormal distribution might be a good fit. This seems reasonable, and the lognormal of course is extremely heavy tailed.
On the other hand, one problem with this is that seeing a single trajectory example doesn’t give one much evidence for any disjunctive/additive components in the distribution. These would be any independent alternate developmental pathways which could bypass the specific developmental chokepoints we see in our single example history.
Another way of thinking about the filter/steps is as a continuous developmental trajectory. We have a reasonable good idea of one sample trajectory—the history of our solar system—and we want to determine if this particular civilization-bearing subspace we are in is like the main sequence or more like a tightrope.
If the development stages have lots of conjuctive/multiplicative dependencies (for example: early life requires a terrestrial planet in the habitable zone with the right settings for various parameters), then a lognormal distribution might be a good fit. This seems reasonable, and the lognormal of course is extremely heavy tailed.
On the other hand, one problem with this is that seeing a single trajectory example doesn’t give one much evidence for any disjunctive/additive components in the distribution. These would be any independent alternate developmental pathways which could bypass the specific developmental chokepoints we see in our single example history.