Estimating population size with capture-recapture

Notebook proposal

Title: Estimating population size with capture-recapture

Why should this notebook be added to pymc-examples?

There are few notebooks on ecology in the examples gallery. While most ecologists do Bayesian statistics via R (e.g., with Stan, Nimble, or BUGS/JAGS), some might be interested in what PyMC has to offer. Moreover, many ecological models involve discrete latent states, and thus might be a good examples for showcasing pymc_extras.marginalize().

I propose adding a notebook about estimating the size of a closed population with capture-recapture, one of the most common tasks in ecology. This would be a great example for demonstrating pymc_extras.recover_marginals() and az.compare(). Moreover, capture-recapture is also used in epidemiology and public policy to estimate the size of hard to reach populations (e.g., the unhoused).

Suggested categories:

• Level: intermediate
• Diataxis type: How-to

Related notebooks

These models are quite similar to the occupancy model presented in this notebook. Nevertheless, the inferential goals are completely different, and would thus showcase different aspects of PyMC. For example, this notebook would make heavy use of pymc_extras.recover_marginals(), since the objective is to estimate the posterior of abundance (i.e., the sum of the discrete latent state).

References

This notebook on closed capture-recapture

Royle, J.A., 2009. Analysis of capture–recapture models with individual covariates using data augmentation. Biometrics, 65(1), pp.267-274.

Start by reading the related occupancy notebook and the linked closed capture-recapture reference. Build the proposed intermediate How-to notebook around closed-population capture-recapture, using pymc_extras.recover_marginals() and az.compare() as described; it is done when the notebook estimates posterior abundance and fits the suggested examples-gallery categories.