Abstract:
Estimating the risk, P(X> Y), in probabilistic environmental risk assessment of
nanoparticles is a problem when confronted by potentially small risks and small
sample sizes of the exposure concentration X and/or the effect concentration
Y. This is illustrated in the motivating case study of aquatic risk assessment of
nano-Ag. A non-parametric estimator based on data alone is not sufficient as it
is limited by sample size. In this paper, we investigate the maximum gain possible
when making strong parametric assumptions as opposed to making no parametric
assumptions at all.We compare maximum likelihood and Bayesian estimators with
the non-parametric estimator and study the influence of sample size and risk on the
(interval) estimators via simulation.We found that the parametric estimators enable
us to estimate and bound the risk for smaller sample sizes and small risks. Also, the
Bayesian estimator outperforms the maximum likelihood estimators in terms of
coverage and interval lengths and is, therefore, preferred in our motivating case study.
