Capture-Recapture With Covariates: The Bayesian Logistic Capture-Recapture Model With Extensions

Abstract

Capture-Recapture methods are used to estimate the size of a finite population from at least two incomplete, matched lists. These methods are useful when conducting a census is impossible or infeasible, but instead a researcher may find it possible to collect or obtain multiple partial samplings of the population. In this dissertation, I introduce a new approach to CR estimation: Bayesian Logistic Capture-Recapture (BLRCR). The BLRCR method offers several benefits: it accommodates multiple lists, is resistant to sparsity, can be informed through use of priors, and can handle missing covariates on the fly. This method models individual-level heterogeneity in the capture probabilities by incorporating both continuous and discrete covariates. Estimation is performed via a Gibbs sampling algorithm.

Next, I extend the BLRCR methodology in three key directions. First, I explore various parametric and nonparametric distributions for the covariates including the Dirichlet process mixture of normal distributions and the Bayesian Bootstrap distribution. Second, I incorporate latent class intercepts into the model which can account for additional heterogeneity not detectable via covariates. Third, I tackle covariate selection using both a Bayes Factor and regularization approach.

Finally, I demonstrate the usefulness of BLRCR by applying it to three CR datasets. I estimate the number of characters in the DC and Marvel universes, the number of killings during the Kosovo War, and the number of killings during the Colombian Conflict in the Casanare region.