What is uncertainty?

Taxonomy of imperfect knowledge

There are many different decision situations, with different possibilities for characterising our confidence in the available information or in other words the uncertainty. A first distinction is between ignorance as a lack of awareness about imperfect knowledge and uncertainty as a state of confidence about knowledge. Our state of confidence may range from being certain to admitting that we know nothing (of use), and uncertainty may be expressed at a number of levels in between. Regardless of our confidence in what we know, ignorance implies that we can still be wrong (‘in error’). In this respect Brown (2004) has defined a taxonomy of imperfect knowledge as illustrated in Fig. 4.

It is useful in evaluating scientific uncertainty to distinguish between uncertainty about the ‘outcomes’ or scenarios, as possible states of ‘reality’ (mechanisms, events, observations), and uncertainty in terms of ‘probability’ (chance, likelihood, plausibility) for each outcome to occur. If one throws a perfect dice, the outcome is uncertain, but the ‘draw’ of a perfect dice is certain: we know precisely the probability for each of the 6 outcomes, each being 1/6. This is what we mean by ‘uncertainty in terms of probability’. However, the estimates for the probability of each outcome can also be uncertain. If a model study says: “there is a 30% probability that this area will flood two times in the next year”, there is not only ‘uncertainty in terms of probability’ but also uncertainty regarding whether the estimate of 30% is a reliable estimate.

Secondly, it is useful to distinguish between bounded uncertainty, where all possible outcomes are deemed ‘known’ (they can be distinct or indistinct) and unbounded uncertainty, where some or all possible outcomes are deemed unknown. Since quantitative probabilities require ‘all possible outcomes’ of an uncertain event and each of their individual probabilities to be known, they can only be defined for ‘bounded uncertainties’. If probabilities cannot be quantified in any undisputed way, we often can still qualify the available body of evidence for the possibility of various outcomes. Inspired by legal practices, Weiss (2003a, 2003b, + personal communication 2004) developed the following 12 point subjective scale for qualifying evidence that can be used for this purpose:

Fig. 4 Taxonomy of imperfect knowledge resulting in different uncertainty situations (Brown, 2004)

 The bounded uncertainty where all probabilities are assumed known (the blue case in Fig. 4) is often denoted ‘statistical uncertainty’ (e.g. Walker et al., 2003). This is the case that is traditionally addressed in model based uncertainty assessments. It is important to note that this case only constitutes one of many of the decision situations outlined in Fig. 4, and, in many situations, the main uncertainty in a decision situation cannot be characterised quantitatively.