Optimal sample size for estimating the mean concentration of invasive organisms in ballast water via a semiparametric Bayesian analysis

We consider the determination of optimal sample sizes to estimate the concentration of organisms in ballast water via a semiparametric Bayesian approach involving a Dirichlet process mixture based on a Poisson model. This semiparametric model provides greater flexibility to model the organism distribution than that allowed by competing parametric models and is robust against misspecification. To obtain the optimal sample size we use a total cost minimization criterion, based on the sum of a Bayes risk and a sampling cost function. Credible intervals obtained via the proposed model may be used to verify compliance of the water with international standards before deballasting.