qualitative assessment of uncertainties and quantitative assessments wherever possible. Preference should be given to quantitative assessment as the desirable approach, and justification for the use of qualitative instead of quantitative approaches should be provided. For example, it should be explained why the state of science is adequate to characterize a point estimate but not a range of uncertainty if quantitative methods of uncertainty analysis are not used.

A key way forward in quantifying uncertainty is to accept the role of expert scientific judgment. Such judgment is used routinely to make inferences regarding hazard identification and in developing dose-response characterizations of chemicals. The examples of Evans et al. (1994), IEC (2006), and Small (2008) rely on encoding expert judgment as subjective probability distributions to various degrees. The appropriate selection and application of methods for quantifying uncertainty in dose-response relationships are undergoing development and need additional research from which guidance on best practices can be derived. As an example of the exploratory nature of dealing with uncertainty in dose-response relationships, the 2007 Resources for the Future workshop “Uncertainty Modeling in Dose Response: Dealing with Simple Bioassay Data, and Where Do We Go from Here?” explored a variety of methods for quantifying uncertainty and the needed role of qualitative assessment to deal with aspects of dose-response modeling that are believed not to be amenable to quantification. Some quantitative techniques that were explored were bootstrap simulation and probabilistic inversion with isotonic regression and Bayesian-model averaging to deal with uncertainty in model structure. However, although there is not yet a default method for quantifying uncertainty in dose-response relationships, EPA can and should review and adopt or adapt various methods that are being explored in the scientific community, taking particular note of the possibilities for combining expert judgment and data with Bayesian approaches.

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