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Your comment made me think of an interesting story and a funfact. During WW2, allies tried to guess the number of German tanks by observing the serial numbers
by emil-lp 1y ago
Your comment made me think of an interesting story and a funfact.
During WW2, allies tried to guess the number of German tanks by observing the serial numbers on captured tanks.
https://en.m.wikipedia.org/wiki/German_tank_problem https://en.m.wikipedia.org/wiki/German_tank_problem
If, say, the serial numbers are unique, and come in sequence, if the five first numbers you see are all less than 100, it's a far chance that there aren't produced 200 tanks. (Provided some assumptions, of course.)
The funfact is that you get different results if you follow the frequentist or the Bayesian approach.
- edbaskerville 1y agoThe Bayesian results will depend on the prior. They use a uniform distribution over # tanks produced, in the limit of the distribution's maximum -> infinity. Is that reasonable? Something more constrained might be better, maybe a gamma-Poisson prior with gamma mean based on some plausible estimate of production rate. (The frequentist/Bayesian estimates should converge as you collect more observations.)