| In this thesis we examine Bayesian methods for sample size determination when sampling from two Poisson distributions with underreported data. We will estimate sample size requirements for a credible set of specified length using an average length criterion (ALC). To compare the two distributions, we use the quantity lambda1--lambda2. A closed form of the posterior of lambda is computationally difficult so it will be approximated. For the estimation, we discuss a normal approximation and a Markov Chain Monte Carlo (MCMC) simulation with a Gibbs sampler. We generate three data sets through our simulation and graph the results. We then fit these graph points with a logarithmic regression curve. From the regression curve we can determine sample sizes needed for a credible set of any specified length. |
