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- W2531629610 abstract "The Hazardous Concentration to x% of an assemblage (HCx) of biological species is the environmental concentration which for a randomly selected species from the assemblage yields an x% probability of violating the species’ toxicological endpoint. Probabilistic methods for estimating the HCx appeal to the probabilistic concept of Species Sensitivity Distributions (SSDs) – a statistical proxy description of interspecies variation within the assemblage. A commonly used estimator class, derived by Aldenberg and Jaworska (2000; Ecotoxicol Environ Saf 46: 1-18), appealed to classical sampling theory, but also coincided with a Bayesian estimator. Two popular estimators from the class are the 50% and 95% (one-sided) underestimate of the HCx. However, whilst choice of x can have ecological significance, choice of confidence remains arbitrary. We reduce the problem to a Bayesian decision theoretic one; and show that their estimator class is equivalent to Bayes Rules under a class of (a-) symmetric linear loss functions, parameterised by the relative cost of over-estimation to under-estimation. A loss function in this sense measures the ‘cost’, which needn’t be monetary, of over- and under-estimation of the HCx estimator. Bayes rules are estimators which minimise expected loss with respect to the posterior SSD – updated with respect to the toxicity data. This potentially opens the way for high-stakes realism to be incorporated into risk assessments. We propose an alternative loss function known as Scaled LINear Exponential (LINEX) which is non-linearly asymmetric in a precautionary way, such that overestimation and underestimation are punished at an exponential and linear rate respectively. We use this loss function to derive an alternative class of HCx estimators." @default.
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- W2531629610 date "2009-01-01" @default.
- W2531629610 modified "2023-09-26" @default.
- W2531629610 title "On the application of loss functions for determining hazardous concentrations" @default.
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