Sample size for estimating organism concentration in ballast water: A Bayesian approach

Estimation of microorganism concentration in ballast water tanks is important to evaluate and possibly to prevent the introduction of invasive species in stable ecosystems. For such purpose, the number of organisms in ballast water aliquots must be counted and used to estimate their concentration with some precision requirement. Poisson and negative binomial models have been employed to describe the organism distribution in the tank, but determination of sample sizes required to generate estimates with pre-specified precision is still not well established. A Bayesian approach is a flexible alternative to accommodate adequate models that account for the heterogeneous distribution of the organisms and may provide a sequential way of enhancing the estimation procedure by updating the prior distribution along the ballast water discharging process. We adopt such an approach to compute sample sizes required to construct credible intervals obtained via two optimality criteria that have not been employed in this context. Such intervals may be used in the decision with respect to compliance with the D-2 standard of the Ballast Water Management Convention. We also conduct a simulation study to verify whether the credible intervals obtained with the proposed sample sizes satisfy the precision criteria.