Bayesian credible intervals for the ratio of two independent poisson rates using data with under-reporting

In this paper, we construct Bayesian credible intervals using an MCMC method for the ratio of two independent Poisson rates with under-reported data. We acquire an identifiable model by using informative priors on an adequate number of model parameters to confirm that a considerable difference occurs in the credible intervals when we account for under-reporting as opposed to Bayesian intervals for the rate ratio that omit under-reporting. We also employ Monte Carlo simulations to examine the prior robustness of our Bayesian intervals. Additionally, we derive a closed form posterior distribution for the rate ratio of two independent priors, and show that informative priors placed on the primary Poisson rates have a greater effect on the posterior density for the ratio of independent Poisson rates with under-reported data than informative priors placed on the remaining model parameters.