David Shor writes:
I’m working on a projection system on election night, and came across a case where I have a binomial distribution with an unknown number of trials.
Is there a good conjugate prior in such a situation?
My reply: There are some articles on this by Adrian Raftery in the late 1980s, you can find references in Bayesian Data Analysis, including a homework assignment in chapter 3, I believe.
Poisson with a gamma conjugate as a close approximation?
I've actually written up a solution to that homework problem, which I can make available to those interested.
Raftery's noninformative prior isn't defined directly on the number of trials N. If I've done the math correctly, it is equivalent to p(N) proportional to 1/N.