Whereof one cannot speak: When input distributions are unknown

One of the major criticisms of probabilistic risk assessment is that the requisite input distributions are often not available. Several approaches to this problem have been suggested, including creating a library of standard empirically fitted distributions, employing maximum entropy criteria to synthesize distributions from a priori constraints, and even using ‘default’ inputs such as the triangular distribution. Since empirical information is often sparse, analysts commonly must make assumptions to select the input distributions without empirical justification. This practice diminishes the credibility of the assessment and any decisions based on it. There is no absolute necessity, however, of assuming particular shapes for input distributions in probabilistic risk assessments. It is possible to make the needed calculations using inputs specified only as bounds on probability distributions. We describe such bounds for a variety of circumstances where empirical information is extremely limited, and illustrate how these bounds can be used in computations to represent uncertainty about input distributions far more comprehensively than is possible with current approaches.