A hierarchical Bayesian model for extreme pesticide residues

The number of residue measurements in an individual field trial, carried out to provide data for a pesticide registration for a particular crop, is generally too small to estimate upper tails of the residue distribution for that crop with any certainty. We present a new method, using extreme value theory, which pools information from various field trials, with different crop and pesticide combinations, to provide a common model for the upper tails of residue distributions generally. The method can be used to improve the estimation of high quantiles of a particular residue distribution. It provides a flexible alternative to the direct fitting of a distribution to each individual dataset, and does not require strong distributional assumptions. By using a hierarchical Bayesian model, our method also accounts for parameter uncertainty. The method is applied to a range of supervised trials containing residues on individual items (e.g. on individual apples), and the results illustrate the variation in tail properties amongst all commodities and pesticides. The outputs could be used to select conservative high percentile residue levels as part of a deterministic risk assessment, taking account of the variability between crops and pesticides and also the uncertainty due to relatively small datasets.