Extensions to the multiplier method for inferring population size

Estimating population size is an important task for epidemiologists and ecologists alike, for purposes of resource planning and policy making. One method is the "multiplier method" which uses information about a binary trait to infer the size of a population. The first half of this thesis presents a likelihood-based estimator which generalizes the multiplier method to accommodate multiple traits as well as any number of categories (strata) in a trait. The asymptotic variance of this likelihood-based estimator is obtained through the Fisher Information and its behaviour with varying study designs is determined. The statistical advantage of using additional traits is most pronounced when the traits are uncorrelated and of low prevalence, and diminishes when the number of traits becomes large. The use of highly stratified traits however, does not appear to provide much advantage over using binary traits. Finally, a Bayesian implementation of this method is applied to both simulated data and real data pertaining to an injection-drug user population. The second half of this thesis is a first systematic approach to quantifying the uncertainty in marginal count data that is an essential component of the multiplier method. A migration model that captures the stochastic mechanism giving rise to uncertainty is proposed. The migration model is applied, in conjunction with the multi-trait multiplier method, to real-data from the British Columbia Centre for Disease Control.Science, Faculty ofStatistics, Department ofGraduat