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February 2021 Sample size for estimating organism concentration in ballast water: A Bayesian approach
Eliardo G. Costa, Carlos Daniel Paulino, Julio M. Singer
Braz. J. Probab. Stat. 35(1): 158-171 (February 2021). DOI: 10.1214/20-BJPS470

Abstract

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.

Citation

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Eliardo G. Costa. Carlos Daniel Paulino. Julio M. Singer. "Sample size for estimating organism concentration in ballast water: A Bayesian approach." Braz. J. Probab. Stat. 35 (1) 158 - 171, February 2021. https://doi.org/10.1214/20-BJPS470

Information

Received: 1 September 2019; Accepted: 1 March 2020; Published: February 2021
First available in Project Euclid: 6 January 2021

MathSciNet: MR4195765
Digital Object Identifier: 10.1214/20-BJPS470

Rights: Copyright © 2021 Brazilian Statistical Association

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Vol.35 • No. 1 • February 2021
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