Estimating Population Size: Animals and Web Pages

Thinking about all of the things in the statistical world that we can estimate, the one that has always perplexed me is estimating the size of an unknown population \(N\). Usually when we compute estimates based on samples, we involve the size of the sample \(n\) somewhere, thus we take “size” for granted — the size of a sample is known. We also make inferences based on sample statistics using theory such as the Central Limit Theorem, but seem to never care about the population size \(N\), we either know it, or assume it is infinite. But, in fields like ecology and environmental studies, this attitude of gluttony is dangerous!

In the summers I spend a lot of time in the Eastern Sierra where there are deer and bears. These animals are so large that we cannot consider their population in the area to be infinite (like we may with ants or bacteria). A matter of fact, one of our local animal behavior specialists knows the exact number of bears that live in my mountain community. I always had just assumed he spent all day tracking down the local bears and marking them with radio collars. There must be some way […]