Bayesian sample size determination for sampling from two Poisson distributions with underreporting

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.