The concept of fiducial inference can be outlined by comparing its treatment of the problem of [[interval estimation]] in relation to other modes of statistical inference.
*A [[confidence interval]], in [[frequentist inference]], with [[coverage probability]] ''γ'' has the interpretation that among all confidence intervals computed by the same method, a proportion ''γ'' will contain the true value that needs to be estimated. This has either a repeated sampling (or [[frequency probability|frequentist]]) interpretation, or is the probability that an interval calculated from yet-to-be-sampled data will cover the true value. However, in either case, the probability concerned is not the probability that the true value is in the particular interval that has been calculated since at that stage both the true value and the calculated are fixed and are not random.
*[[Credible interval]]s, in [[Bayesian inference]], do allow a probability to be given for the event that an interval, once it has been calculated does include the true value, since it proceeds on the basis that a probability distribution can be associated with the state of knowledge about the true value, both before and after the sample of data has been obtained.