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

Article type: Research Article

Authors: Greer, Brandi A. | Young, Dean M. | Young, Philip D.^{; *}

Affiliations: Baylor University, Waco, TX, USA

Correspondence: [*] Corresponding author: Philip D. Young, Baylor University, P.O. Box 97140, Waco, TX 76798, USA. Tel.: +1 254 710 6183; Fax: +1 254 710 4477; E-mail: [email protected].

Abstract: 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.

Keywords: Misclassification, identifiability, count data

DOI: 10.3233/MAS-2012-0231

Journal: Model Assisted Statistics and Applications, vol. 7, no. 2, pp. 131-142, 2012