Bayesian Sample Size Determination for Estimating a Poisson Rate with Underreported Data

Abstract

We consider the problem of estimating the required sample size to achieve a credible set of specified length for the Poisson model with underreporting using an average coverage criterion. The actual posterior is found to be computationally taxing; thus we approximate via two approaches. The first method approximates the marginal and posterior densities with more tractable densities. The second is a Monte Carlo approach. We provide a limited study of the effect of the prior information and the magnitude of the reporting probability.

Key Words:

• Error prone data
• Posterior approximation
• BB/NBD
• Hypergeometric function

Acknowledgment

The authors are grateful to an anonymous referee whose comments improved the paper.