To count an animal population if you can't catch them all: capture some, mark them, release, and capture again. The ratio of new vs already seen tells you something about the total number. Shown here is iterated mark-and-recapture with a Bayesian updates to belief about pop size
The left side shows a crude simulation of animals moving around, which are periodically captured. Colour indicates number of times captured. Right side is a distribution describing belief over the population size.
It's funny that the first 'measurement' is much less informative than subsequent ones: it just tells you that the population is at least as large as the number of animals you've captured.
Assumption made here: the animals move around enough between measurements that you can treat each capture event as a random selection from the population, independent of the previous capture
