Determining environmental standards using bootstrapping, bayesian and maximum likelihood techniques: a comparative study

Environmental standards must be set in ways which give full recognition to all sources of uncertainty and variability of the toxicity data used to derive these standards. Toxicity data such as NOECs form a variability distribution describing species sensitivity distribution (SSD). In EU environmental regulations the 5th-percentile of SSD is used to set the quality criteria. In this paper, a comparison is made between the application of techniques characterising uncertainty and variability (bootstrap, maximum likelihood estimation (MLE) and Bayesian approaches) using small toxicity data sets to calculate the 5th-percentile. Estimating lower and upper uncertainty bounds of a specific percentile gives different results when different methods are used. Bayesian and MLE methods were found to be superior to parametric bootstrapping because they are easier to use and not so computationally intensive.