On the application of loss functions for determining hazardous concentrations

Hickey, Graeme ORCID: 0000-0002-4989-0054, Craig, Peter S and Hart, Andy
(2009) On the application of loss functions for determining hazardous concentrations. [Poster]

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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.

Item Type: Poster
Depositing User: Symplectic Admin
Date Deposited: 27 May 2015 08:32
Last Modified: 02 Apr 2021 07:17
URI: https://livrepository.liverpool.ac.uk/id/eprint/2012065