A united interpretation of different uncertainty intervals

The frequentist and Bayesian philosophies of statistical inference require different approaches to the calculation of an interval of uncertainty for a measurand. A frequentist (or classical) interval will have an associated confidence level, p, that is the probability of generating an interval enclosing the value of the measurand. A Bayesian interval will have an associated credible level, p, that is a 'degree-of-belief' that the value of the measurand subsequently lies within the interval. Since potential users are not primarily concerned with the method of analysis, a shared interpretation of the information given to them seems desirable. We obtain such an interpretation by recognising that in either case p is the proportion of independent intervals calculated over time that contain their respective measurands. This interpretation is also useful in explaining an interval calculated according to the procedure of Guide to the Expression of Uncertainty in Measurement.