Year of Publication

2017

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Simon Bonner

Second Advisor

Dr. Arnold Stromberg

Abstract

The extension of the CJS model to include individual, continuous, time-varying covariates relies on the estimation of covariate values on occasions on which individuals were not captured. Fitting this model in a Bayesian framework typically involves the implementation of a Markov chain Monte Carlo (MCMC) algorithm, such as a Gibbs sampler, to sample from the posterior distribution. For large data sets with many missing covariate values that must be estimated, this creates a computational issue, as each iteration of the MCMC algorithm requires sampling from the full conditional distributions of each missing covariate value. This dissertation examines two solutions to address this problem. First, I explore variational Bayesian algorithms, which derive inference from an approximation to the posterior distribution that can be fit quickly in many complex problems. Second, I consider an alternative approximation to the posterior distribution derived by truncating the individual capture histories in order to reduce the number of missing covariates that must be updated during the MCMC sampling algorithm. In both cases, the increased computational efficiency comes at the cost of producing approximate inferences. The variational Bayesian algorithms generally do not estimate the posterior variance very accurately and do not directly address the issues with estimating many missing covariate values. Meanwhile, the truncated CJS model provides a more significant improvement in computational efficiency while inflating the posterior variance as a result of discarding some of the data. Both approaches are evaluated via simulation studies and a large mark-recapture data set consisting of cliff swallow weights and capture histories.

Digital Object Identifier (DOI)

https://doi.org/10.13023/ETD.2017.250

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