A Bayesian Hierarchical Model for Poisson Rate and Reporting‐probability Inference Using Double Sampling

Summary We analyse a combination of errant count data subject to under‐reported counts and inerrant count data to estimate multiple Poisson rates and reporting probabilities of cervical cancer for four European countries. Our analysis uses a Bayesian hierarchical model. Using a simulation study, we demonstrate the efficacy of our new simultaneous inference method and compare the utility of our method with an empirical Bayes approach developed by Fader and Hardie ( J. Appl. Statist. , 2000).