Electronic Thesis and Dissertation Repository

Thesis Format

Monograph

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

Bonner, Simon

Abstract

Mark-recapture methods play a key role in ecological studies monitoring wild animal populations. One consideration in analyzing mark-recapture data is individual variation in the detection rate. Classical methods for modelling heterogeneity require numerical integration and may be computationally intensive. This thesis presents a novel approach based on the h-likelihood to remedy such difficulties by avoiding numerical integration.

First, I present the h-likelihood approach for fitting the fundamental model describing individual heterogeneity in mark-recapture studies. The conditional likelihood approach allows the model to be regarded as a generalized linear mixed model (GLMM). I construct the h-likelihood for the model in the context of this GLMM. The population size is estimated via the Horvitz-Thompson estimator.

Second, I extend my approach to fit advanced models accounting for individual heterogeneity along with variation over time and individuals’ trap responses. The conditional likelihood approach enables these models to be treated as vector GLMMs. The approach from the first project is adapted to fit these models with multi-dimensional response variables. The Horvitz-Thompson estimator is again employed to estimate the population size.

Finally, I develop the h-likelihood approach to fit more flexible models describing individual heterogeneity. As standard models assume a linear relationship, I apply the structure of generalized additive models through B-spline, which can be considered as a GLMM with the conditional likelihood penalized for roughness. Again, I apply the h-likelihood to fit this model and to estimate the population size using the Horvitz-Thompson estimator.

Summary for Lay Audience

Mark-recapture methods have played a key role in ecological studies monitoring populations of wild animals, including those threatened by human disturbance. One consideration in the analysis of mark-recapture data is individual variations in the rate of detecting individuals. Failure to account for a variation can lead to biased inference, but classical methods for modelling heterogeneity require numerical integration and can be computationally intensive or numerically unstable. This thesis develops a novel approach based on the h-likelihood, which can remedy such difficulties by avoiding any numerical integration.

In the first project, I present my h-likelihood for fitting the fundamental model describing individual heterogeneity in mark-recapture studies. The conditional likelihood approach allows the model to be considered as a generalized linear mixed model (GLMM), and building on this connection, I construct the h-likelihood for the model in the context of the GLMM. In addition, I derive a bias correction for the model parameters and develop inference for the population size via the Horvitz-Thompson estimator.

My second project extends my approach to fit advanced models accounting for individual heterogeneity in which the capture probability may also depend on time and individuals’ trap responses. The conditional likelihood approach enables these models to be treated as vector GLMMs. The h-likelihood approach from the first project is then extended to fit these models by allowing the response variables to be multi-dimensional. Bias correction is again considered, and the Horvitz-Thompson estimator is employed for estimating the population size as before.

Finally, I develop my h-likelihood approach to fit more flexible models describing individual heterogeneity. Standard models assume a linear relationship on some scale of the detection rate. The model I consider relaxes this assumption by applying the structure of generalized additive models via penalized spline, which can be regarded as a GLMM when the conditional likelihood is penalization for roughness. I apply the h-likelihood approach to fit this model and again estimate the population size using the the Horvitz-Thompson estimator.

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