Efficient Bayesian Estimation for Open Population Capture-Recapture Models Without Data Augmentation

Devin Johnson, Shelbie K. Ishimaru, Janelle J. Gardner

1. Bayesian estimation of abundance with capture-recapture data has been dominated for nearly 20 years by the parameter-expansion data-augmentation (PX-DA) ap- proach. The PX-DA approach expands the parameter set to include the latent true states of the individuals. PX-DA allows straightforward coding of models in MCMC software such as JAGS (Just Another Gibbs Sampler) or nimble, however, this ap- proach can be computationally demanding for large or low detectability populations.
2. We develop a collapsed Gibbs sampler version of the PX-DA approach to reduce com- putational burden when using Markov Chain Monte Carlo (MCMC) to fit Jolly-Seber (JS) models. Using the collapsed sampler, no parameter expansion or data augmen- tation is needed. Two of the main computational benefits are: (1) the MCMC only needs to iterate over unique capture-histories and (2) the MCMC can be divided into 2 stages where the second stage sampler can be run in parallel. We provide an R pack- age nimbleJSextras that uses the functionality of the nimble and nimbleEcology packages to perform MCMC analysis for JS models with the same ease for practi- tioners the PX-DA approach.
3. Using the nimbleJSextras package, we analyzed two real data sets to illustrate the method. First we analyzed the classic dipper data using per capita recruitment parameterization. We compared the collapsed sampler to PX-DA. In the second example we analyzed a data set of 5,271 female nesting green turtles in the Northwest Hawaiian Islands over a 44 year period that contained time by individual behavioral effects induced by capture procedures.
4. In the dipper analysis the relative speed of the MCMC compared to the PX-DA sam- pler depended on the number of augmented individuals, slower for 300 augmented individuals and faster for 1,000 individuals. Convergence metrics showed slightly quicker convergence of the collapsed MCMC than the PX-DA sampler. The full 2- stage collapsed sampler ran in only 1/10 the amount of time needed for the PX-DA sampler. The more complex green turtle data finished in < 3.5 hours illustrating that relatively large, long-term data can be analyzed efficiently even with a complex capture probability model using the 2-stage collapsed sampler. Moreover, trial anal- yses are not necessary to determine an adequate number of augmented individuals.