Improving isochron calculations with robust statistics and the bootstrap

Typical isochron calculations involve using a least squares analysis of the data. If the scatter about a line through the data is perfectly Gaussian, then least squares provides an optimal handling of the data. However, if the data are Gaussian only in the centre of the distribution, but depart from it only slightly in the tails of the distribution, then least squares is not optimal and can easily degrade seriously. For the size of datasets that are used in isochron calculations, such non-Gaussian behaviour is impossible to test for. This is important because there are numerous sources of uncertainty which might result in subtly non-Gaussian behaviour. Therefore, to defend against degradation, it is proposed that isochron calculations be modified by the use of a robust statistical method so that non-Gaussian tail behaviour can be accounted for. For data that are actually Gaussian-distributed, the new isochron calculation method will generally give identical results to least squares. The improvement given by the new method is illustrated by the use of simulations.