Age Reporting of Very Old Samples

Problems of the statistical interpretation of radiocarbon age measurements of old samples are discussed, based on the notion of fiducial probability distribution. A probability density function of age has been given. A detailed discussion of different facets of the probability distribution of age has led us to the confirmation of the use of 2σ as the best limiting value between the regions of finite and infinite dates. It has been proposed to make use of the principle of constant probability P = 0.68 in the regions of both finite and infinite ages instead of the criterion N + kσ.

On Sprott's Example of an Ancillary Statistic

For statistical inference on the unknown parameter θ of a probability distribution with a known form of its density function f(x | θ), the late Sir R. A. Fisher suggests that inference should be based on the observed value of a sufficient statistic when it exists. In the absence of a sufficient statistic, fiducial probability statements about θ can still be made, according to Fisher, if we can find an ancillary statistic so that "the most likely estimate could be made exhaustive by means of the ancillary values" [1, p. 138].