| Capture-recapture models are widely used to estimate population size and demographic parameters for wild animal populations. These models have recently been applied to other research areas. For example, they are used to study the total number of people with a certain disease in epidemiology, to estimate the number of homeless, drug addicts, or dog bites in social science and to estimate the total number of bugs in a program in computer science.In the capture-recapture experiment, the population is often sampled several times. Each time, every unmarked animal is uniquely marked, previously marked animals have their captures recorded and all animals are released back to the population. There are three possible factors that affect the capture probabilities: time (capture probabilities vary from sample to sample), behavioral response (a trap response of animals to the first capture) and heterogeneity (different animals have intrinsically different capture probabilities). There are eight models regarding possible combinations of these factors, M0, Mt, Mb, Mh, Mtb, Mth, Mbh and M tbh (Otis et al., 1978).The main focus of our study is to estimate the population size under capture-recapture models in a Bayesian framework. This work consists of four parts. In Chapter 2, we study the model Mt, which has only the time effect. Some non-informative priors are used to estimate the population sizes. In Chapter 3, we incorporate both time and behavioral response to the study and investigate the model Mtb. The model Mtbh, which includes time, behavioral response and heterogeneity effects, is considered in Chapter 4. Log-linear transformation and Bayesian hierarchical priors are used to estimate the population size. In Chapter 5, we study an application of capture-recapture models in an epidemiological study. They are used to estimate the total number of patients in a certain research area. The computations are performed via Markov chain Monte Carlo (MCMC) methods, such as Gibbs sampling, Metropolis-Hastings algorithm and Gilk's adaptive-rejection sampling techniques. Finally, we describe some possible future studies in Chapter 6. |
