From error ellipse to Bayesian estimation: Strategies for optimizing T-W diagrams in UPb dating

This study examines the application of the T-W diagram (Tera-Wasserburg Concordia Diagram) in uranium‑lead (UPb) isotope dating technology, especially for samples containing common lead. The core of the research lies in evaluating and optimizing the accuracy, precision, and determination of confidence intervals of T-W diagram dating. We propose a new formula based on the geometric mean method for correcting the calculation of error ellipses to reduce bias from high data noise levels. The study further elaborates on the application of the error-correlated independent weighted least squares method in determining the confidence intervals of linear models and intersection ages. Through simulation analysis, we evaluate the performance of least square methods in terms of dating accuracy and precision with both well-distributed and poorly distributed data. In view of the limitations of least square methods, a Bayesian method based on intercept constraints or the evolution model of terrestrial common lead is proposed, significantly improving the accuracy, precision, and success rate of dating analysis. The new methodology of this study not only provides a more reliable analytical tool for the field of radiometric dating, but is also applicable to single-point age analysis.