There is a number $N$ of balls in the urn that is growing in real time, and the number $R$ of red balls and $N-R$ white ones. We make a ‘pre-data’ inference about what kind of mix of $r$ red, $n−r$ white we were likely to get on drawing $n$ of them. Our ‘post-data’ problem: the data $D ≡ (n, r)$ are known, but the contents $(N, R)$ of the urn are not.
If $N$ is growing at an unknown rate in real time, let us say for case of conjecture that $N'$ is defined by some unknown curve for instance:
How might one go about sampling the urn to guarantee that sample is random and make $n$ a sufficient sample of $N$ which is unknown and growing?
My current solution to this is to take the first 10 from the urn, which was sufficiently shaken, every 100 balls that are added to the urn. This seems insufficient to me.
PS: I re-framed the opening problem from Probability Theory by ET Jaynes' from Chapter 6. The original problem was the same but $N$ was not growing in real time. For the purposes of my problem it is, but the rest of the problem is the same. 10% is arbitrary, at most I just want whatever happens to be sufficient.