Statistical Modelling 16 (1) (2016), 24–46

Sparse Bayesian modelling of underreported count data

Michaela Dvorzak
Joanneum Research,
Graz,
Austria
e-mail: michaela.dvorzak@joanneum.at

Helga Wagner
Department of Applied Statistics,
Johannes Kepler University,
Linz,
Austria


Abstract:

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.

Keywords:

MCMC; parameter identification; Poisson regression; underreporting; variable selection.

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