A new Bayesian approach toward improved regression of low-count U-Pb geochronology data generated by LA-ICPMS

U-Pb dating of hydrogenic and fossil material can be a significant challenge because samples often contain low U levels and variable amounts of non-radiogenic Pb. Line scans using LA-ICPMS provide the widest range of ratios available for defining the radiogenic to common Pb mixing line, hence the best age estimate, but extracting this information requires processing many low-count data. Conventional least-squares regression of ratios based on such data can give inconsistent results. A new approach is introduced where data are regressed as count rates in a 3D space rather than ratios on a 2D plot. This is a maximum likelihood approach in that mixing planes covering a range of ages and common Pb-207/Pb-206 ratios (PbC) are compared to the data set and used to determine a relative probability density surface whose maximum should fix the best-fit age and common Pb-207/Pb-206 ratio. 95% confidence errors are determined from T and PbC values that cut off 2.5% of the area to the left and right of 2D plots generated by integration of the 3D plot over PbC and age, respectively. Results from a rugose coral fossil show that this approach gives age results similar to regressions of concordia data and more accurate than Tera-Wasserburg regressions on data from natural samples. Tests on randomly generated synthetic data do not show significant discrepancy between Isoplot ages but they do between values of PbC. The 3D approach is the only one that gives accurate results for both age and PbC.