Subjective Probability-Based Scenarios for Uncertain Input Parameters

Risk analysis often depends on complex, computer-based models to describe links between policies (e.g., required emission-control equipment) and consequences (e.g., probabilities of adverse health effects). Appropriate specification of many model aspects is uncertain, including details of the model structure; transport, reaction rate, and other parameters; and application specific inputs such as pollutant-release rates. Because these uncertainties preclude calculation of the precise consequences of a policy, it is important to characterize the plausible range of effects. In principle, a probability distribution function for the effects can be constructed using Monte Carlo analysis, but the combinatorics of multiple uncertainties and the often high cost of model runs quickly exhaust available resources. This Note presents and applies a method to choose sets of input conditions (scenarios) that efficiently represent knowledge about the joint probability distribution of inputs. A simple score function approximately relating inputs to a policy-relevant output — in this case, globally averaged stratospheric ozone depletion — is developed. The probability density function for the score-function value is analytically derived from a subjective joint probability density for the inputs. Scenarios are defined by selected quantiles of the score function. Using this method, scenarios can be systematically selected in terms of the approximate probability distribution function for the output of concern, and probability intervals for the joint effect of the inputs can be readily constructed.