Quantifying Uncertainty

Natural language is not adequate for propagating and communicating uncertainty. To illustrate, consider the U.S. National Research Council 2010 report Advancing the Science of Climate Change America’s Climate Choices: Panel on Advancing the Science of Climate Change; National Research Council, 2010). Using the AR4 calibrated uncertainty language, the NRC is highly confidente that (1) the Earth is warming and that (2) most of the recente warming is due to human activities.

What does the second statement mean? Does it mean the NRC is highly confident that the Earth is warming and the recent warming is anthropogenic or that, given the Earth is warming, are they highly confident humans cause this warming? The latter seems most natural, as the warming is asserted in the first statement. In that case the ‘high confidence’ applies to a conditional statement. The probability of both statements being true is the probability of the condition (Earth is warming) multiplied by the probability of this warming being caused by humans, given that warming is taking place. If both statements enjoy high confidence, then in the calibrated language of AR4 where high confidence implies a probability of 0.8, the statement that both are true would only be “more likely than not” (0.8 x 0.8 = 0.64).

Qualitative uncertainty analysis easily leads the unwary to erroneous conclusions. Interval analysis is a semiqualitative method in which ranges are assigned to uncertain variables without distributions and can mask the complexities of propagation, as attested by the following statement in an early handbook on risk analysis: “The simplest quantitative measure of variability in a parameter or a measurable quantity is given by an assessed range of the values the parameter or quantity can take. This measure may be adequate for certain purposes (e. g., as input to a sensitivity analysis), but in general it is not a complete representation of the analyst’s knowledge or state of confidence and generally will lead to an unrealistic range of results if such measures are propagated through na analysis”, (U. S. NRC, 1983, Chapter 12, p.12).

The sum of 10 independent variables each ranging between zero and ten, can assume any value between zero and 100. The upper (lower) bound can be attained only if ALL variables take their maximal (minimal) values, whereas values near 50 can arise through many combinations. Simply stating the interval [0, 100] conceals the fact that very high (low) values are much more exceptional than central values. These same concepts are widely represented throughout the uncertainty analysis literature. According to Morgan and Henrion (1990): “Uncertainty analysis is the computation of the total uncertainty induced in the output by quantified uncertainty in the inputs and models […] Failure to engage in systematic sensitivity and uncertainty analysis leaves both analysts and users unable to judge the adequacy of the analysis and the conclusions reached”, (Morgan and Henrion, 1990, p. 39).

Capítulo 2: Integrated Risk and Uncertainty Assessment of Climate

Change Response Policies, In: Climate Change 2014, p. 174