Measurement Uncertainty - Alternative Perspective

Alternative Perspective

Most of this article represents the most common view of measurement uncertainty, which assumes that random variables are proper mathematical models for uncertain quantities and simple probability distributions are sufficient for representing all forms of measurement uncertainties. In some situations, however, a mathematical interval rather than a probability distribution might be a better model of uncertainty. This may include situations involving periodic measurements, binned data values, censoring, detection limits, or plus-minus ranges of measurements where no particular probability distribution seems justified or where one cannot assume that the errors among individual measuresments are completely independent.

A more robust representation of measurement uncertainty in such cases can be fashioned from intervals. An interval is different from a rectangular or uniform probability distribution over the same range in that the latter suggests that the true value lies inside the right half of the range with probability one half, and within any subinterval of with probability equal to the width of the subinterval divided by b–a. The interval makes no such claims, except simply that the measurement lies somewhere within the interval. Distributions of such measurement intervals can be summarized as probability boxes and Dempster-Shafer structures over the real numbers, which incorporate both aleatoric and epistemic uncertainties.