Monte Carlo approach to calculate US-ESR age and age uncertainty for tooth enamel

• USESR program was developed for calculating US-ESR age for tooth enamel.
• This program uses Monte Carlo simulations for age and age uncertainty calculations.
• USESR was applied to a large number of virtual samples designed with measured data.
• Experimental results show that USESR can provide reliable age results.

The combination of electron spin resonance (ESR) and U-series dating approach is increasingly being used to fossil teeth from archaeological sites. A rigorous age uncertainty assessment is needed for this dating method. However, it is difficult to provide partial derivatives of the combined ESR/U-series (US) model, as required by the law of propagation of uncertainties. In this study, we developed a new age calculation MATLAB program, called USESR, using a Monte Carlo approach for estimating the age and the age uncertainty for tooth enamel. Tests have been performed with virtual samples (n = 64). The results suggest that this Monte Carlo approach can provide reliable US-ESR age and reduced age uncertainty in comparison with those obtained by the routinely used program, DATA. The results also show that the new program has higher tolerance limits of U-series disequilibrium than the DATA program for US-ESR age calculations.