Bayesian inference for comparing two Poisson rates using data subject to underreporting and validation data

We derive a new Bayesian credible interval estimator for comparing two Poisson rates when counts are underreported and an additional validation data set is available. We provide a closed-form posterior density for the difference between the two rates that yields insightful information on which prior parameters influence the posterior the most. We also apply the new interval estimator to a real-data example, investigate the performance of the credible interval, and examine the impact of informative priors on the rate difference posterior via Monte Carlo simulations.