Earlier quoted context omitted.
The article is not about picking parameters. The article is one meta layer up from that; they examine the distribution of parameters. I can't guarantee this is novel paper in general, but it's not something I've seen treated this formally before. I mean, it roughly conforms to what I've been saying for a while, but I only worked the math very intuitively and in a manner that could have been flawed, so I get no credit…
OK, picking distributions. I can't imagine that there's enough data to even do that.
Generally, these ignorance priors are improper (unnormalizable) distributions. One example is scale parameters, where the approriate prior is 'ds/s', which makes any order of magnitude equally probable. It doesn't have a mean, and it favors small values. A tiny bit of evidence will immediately turn it into a proper posterior distribution; I think this prior has zero information content.
Of course, if one applies that approach to the Drake equation, one ends up with an equally uninformative posterior distribution, unless one can add evidence for each single variable. But that evidence just isn't there for some of them, so the result remains the same: It's impossible to estimate N, but it's probably very small. As it should be, given the total lack of data.