Bayesian sample size for estimating the concentration of organisms in ballast water 1 Introduction

With the growth of maritime traffic and the use of large ships, ballast water has become a leading dispersing agent of harmful organisms (David et al., 2007; Souza et al., 2001). According to Ruiz et al. (2000) human pathogens are also being transported through ballast water. As an example, we mention a cholera epidemic occurred in Peru in 1991 and quickly spread through Latin America (McCarthy et al., 1992). The D-2 Regulation of the International Convention for the Control and Management of Ship Ballast Water and Sediments adopted by the International Maritime Organization (IMO) in 2004 sets upper limits on the concentrations of living organisms in ballast water discharges to which ships must comply with. In particular, this regulation requires that ballast water discharged by ships contain fewer than 10 viable organisms with minimum dimension ≥ 50 μm by m. Because of cost and time restrictions, examination of the entire volume of discharge is not feasible and sampling must be considered. Different approaches to this problem have been considered in the literature. Basurko & Mesbahi (2011) adopted a binomial model, but their results suggest that large volumes of discharged ballast water should be sampled to assure compliance with reasonable accuracy. Miller et al. (2011) employed Poisson distribution models and their approach produced more realistic results. Both approaches, however, are based on the assumption that the organisms concentration is homogeneous in the ballast water tank. This may not be reasonable in practice, as pointed out by Miller et al. (2011) or Carney et al. (2013), among others. More recently, Bierman et al. (2012) and Costa (2013), working independently, suggested negative binomial models that take the expected heterogeneity of the concentration into account. In all cases, issues concerning the implications of statistical “representativeness” of the sample are discussed, without a clear definition of what this means. For the purpose of compliance with the D-2 Regulation, a “representative sample” is one for which the analysis allows an estimation of the true concentration of viable organisms with a given accuracy. Given that accuracy is