PhD Public Lecture (DSAS) - Han Na Kim

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 Horvitz-Thompson estimator.