A Mathematical-Statistical Method for EPMA U-Th-Pb Chemical Age Analysis of Pitchblende

Pitchblende is susceptible to Pb substitution and/or U loss, resulting in deviations in chemical ages determined by the electron probe microanalysis (EPMA) U-Th-^totalPb method. Although previous studies have attempted to correct chemical ages through linear regression, they generally lack a systematic statistical framework, particularly regarding data preprocessing and outlier identification, which limits result reliability. To address these deficiencies, a mathematical-statistics-based workflow for chemical age processing was developed and applied to the Xiwang uranium deposit in the Xiazhuang orefield, northern Guangdong. Spearman rank correlation tests were employed to verify the Pb substitution, while K-means clustering and Gaussian mixture modeling (GMM) were applied to identify latent subgroups within the dataset. After excluding anomalous data, a linear regression model was constructed to extrapolate chemical ages to the point of negligible Pb substitution, thereby estimating pitchblende crystallization ages. The results indicate that the SiO₂ + FeO model provides the best fit, yielding two extrapolated ages of 102.39 ± 5.88 Ma and 56.87 ± 3.61 Ma, corresponding to the second-stage and fourth-stage mineralization events of the Xiazhuang orefield, respectively, both of which have reasonable geological significance. Samples significantly affected by U loss exhibit systematically overestimated chemical ages, whereas GMM decomposition of these data reveals subpopulation ages indicative of complex hydrothermal overprinting. The proposed “statistical analysis–model optimization–geological interpretation” workflow effectively enhances the stability and reliability of EPMA U-Th-^totalPb chemical dating and provides a new methodological and interpretive framework for age determination of pitchblende in granite-related uranium deposits.