Sparse Bayesian modelling of underreported count data

We consider Bayesian inference for regression models of count data subject to underreporting. For the data generating process of counts as well as the fallible reporting process a joint model is specified, where the outcomes in both processes are related to a set of potential covariates. Identification of the joint model is achieved by additional information provided through validation data and incorporation of variable selection. For posterior inference we propose a convenient Markov chain Monte Carlo (MCMC) sampling scheme which relies on data augmentation and auxiliary mixture sampling techniques for this two-part model. Performance of the method is illustrated for simulated data and applied to analyse real data, collected to estimate risk of cervical cancer death.