2
Describing and Propagating Uncertainty
2.1 Methods of Describing Uncertainty
Uncertainty in the true value of any quantity can be described in several different ways depending on the nature of the uncertainty and the depth of understanding of the underlying causes of the uncertainty (Ferson and Ginzburg, 1996).
2.1.1 Uncertainty Intervals and Probability Distributions
If the only available information is that the uncertainty is known to lie within a particular range, the only possible way of describing it is by specifying an uncertainty interval within which the true value must lie. For example, if the uncertainty interval is [a, b], the standard uncertainty ux associated with a quantity x = (a+b)/2 is given by ux = (b−a)/2, where the true value of x = xT is given by xT = x 
ux.
If the uncertainty is known to be a result of random effects, it may be possible for the probability of the quantity having a particular value to be found. In this case, the most probable value of the quantity xm can found from its associated probability density function p(x):
(2.1) 
and, if the distribution is unimodal, a confidence interval I
= [a,b] can be defined that specifies those values of the quantity ...
