Think Bayes, 2nd Edition

Chapter 15. Mark and Recapture

This chapter introduces “mark and recapture” experiments, in which we sample individuals from a population, mark them somehow, and then take a second sample from the same population. Seeing how many individuals in the second sample are marked, we can estimate the size of the population.

Experiments like this were originally used in ecology, but turn out to be useful in many other fields. Examples in this chapter include software engineering and epidemiology.

Also, in this chapter we’ll work with models that have three parameters, so we’ll extend the joint distributions we’ve been using to three dimensions.

But first, grizzly bears.

The Grizzly Bear Problem

In 1996 and 1997 researchers deployed bear traps in locations in British Columbia and Alberta, Canada, in an effort to estimate the population of grizzly bears. They describe the experiment in this article.

The “trap” consists of a lure and several strands of barbed wire intended to capture samples of hair from bears that visit the lure. Using the hair samples, the researchers use DNA analysis to identify individual bears.

During the first session, the researchers deployed traps at 76 sites. Returning 10 days later, they obtained 1,043 hair samples and identified 23 different bears. During a second 10-day session they obtained 1,191 samples from 19 different bears, where 4 of the 19 were from bears they had identified in the first batch.

To estimate the population of bears from this data, we need ...