Estimation of P(X>Y) for Normal Distributions in the Context of Probabilistic Environmental Risk Assessment for Nanoparticles

Organised by Biometris

Fri 30 January 2015 11:00 to 12:00

Venue Radix, gebouwnummer 107
Room W0.1

As is the case for all novel materials, risk assessment (RA) is important for the societal acceptance and safe use of engineered nanoparticles. In order to perform a proper RA, we need knowledge and data on the properties of nanoparticles. This information is hard to come by due to lack of knowledge and technical limitations, resulting in large amounts of uncertainty. When high levels of uncertainty are foreseen, a probabilistic RA is recommended. In probabilistic RA, variability in environmental exposure is quantified by an exposure distribution. Similarly, variability in effect is quantified by a species sensitivity distribution (SSD). The overlap of the exposure distribution and the SSD forms the basis for risk characterization in a probabilistic RA and is defined as the risk probability, R=P(X>Y). In this paper, we consider three parametric estimators of the risk probability. These are the maximum likelihood estimator (MLE), quasi maximum likelihood estimator (QMLE) and Bayesian estimator with a diffuse prior. We also provide the non-parametric empirical estimator as comparison. Monte Carlo simulation was performed for combinations of sample sizes and R values to evaluate the performance of the estimators. We conclude that for small sample sizes the MLE and QMLE give the best results. The non-parametric estimator is incapable of estimating small R values. Even for the largest sample sizes that we used the estimator cannot estimate R values lower than 0.0001. The Bayesian estimator, although very biased for lower sample sizes, has a high accuracy compared to the other estimators for small R values. This could possibly be interesting to explore when a more informative prior is used, based on existing prior knowledge.