Ignorance Is Not Probability

Abstract

The distinction between ignorance about a parameter and knowing only a probability distribution for that parameter is of fundamental importance in risk assessment. Brief dialogs between a hypothetical decisionmaker and a risk assessor illustrate this point, showing that the distinction has real consequences. These dialogs are followed by a short exposition that places risk analysis in a decision-theoretic framework, describes the important elements of that framework, and uses these to shed light on Terje Aven's criticism of nonprobabilistic purely "objective" methods. Suggestions are offered concerning a more effective approach to evaluating those methods.

An Evaluation of the Treatment of Risk and Uncertainties in the IPCC Reports on Climate Change

“…The above analysis provides an example of how to present risk according to the (C’,Q, K) framework. There is an ongoing discussion in the literature concerning this issue of how to represent and express the risks and uncertainties . In its general form this discussion is beyond the scope of this article.…”

Evaluating Uncertainty in Risk-Based Interdependency Modeling With Interval Arithmetic

“…We would argue, similarly to Huber (2010), that the benefits of an informative approach like the Monte Carlo method do not outweigh the potential for making incorrect decisions based on forcing probability distributions when knowledge of those distributions does not exist. The interval approach is convenient when decision-makers are interested, for example, in worst case results only.…”

Interval-valued availability framework for supplier selection based on component importance

“…An approach where these uncertain parameters are described by probability distributions is always preferred when distributions are known, as one could address the problem with, for example, Monte Carlo simulation. However, when such probability distributions are not known, 'forcing' a distribution may do more harm to the decisionmaking process than good (Huber 2010). This is particularly true when developing distributions for failure time or repair time during the requirement development process in system design.…”

“…We instead represent uncertainty in these failure time and repair time parameters with interval values, assuming we can bound the parameters with minimum and maximum values. If we can only assume the upper and lower bounds, we should 'consider what decisions we could reach for all possible values of those data that are consistent with those interval constraints' (Huber 2010). …”