Abstract
SUMMARY Lindley (1958) and Sprott (1960) have proposed several criteria for the satisfactory application of the fiducial method of inference to statistical problems. The criteria are concerned with consistency when there are various ways of applying the method. In sections 1 and 2 these criteria are discussed briefly, and the range of problems that yield fulfilment of the criteria is shown to be considerably larger than that indicated by Lindley and Sprott. A frequency interpretation for a fiducial distribution has been proposed and discussed in two recent papers (Fraser, 1961a, b); this interpretation is available for problems that are invariant in a natural sense under translation and transformation groups. If the purpose of the fiducial method of inference is to produce posterior probability statements about the parameter that have a frequency interpretation and are consistent according to criteria such as Lindley’s and Sprott’s, then the range of validity can be substantially extended by making a small modification to the method; this is discussed in sections 3 to 6.
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