A Bayesian hierarchical age model for optical dating of single grains of quartz

In optical dating, the last time that a sample of sediment was exposed to sunlight is determined by dividing its equivalent dose (De) by the dose rate. For single-grain dating, the sample De is based on the statistical analysis of the distribution of De values estimated for individual grains, whereas the dose rate is usually determined from measurements of the environmental radioactivity of the bulk sample, together with allowances for radiation sources internal to the grains and cosmic rays. Conventionally, the De and dose rate are measured and analysed separately to produce an estimate of the depositional age of a sample, but this approach may result in loss of information because distributions of single-grain De values are influenced by several factors. Existing statistical models do not incorporate all the key information contributing to age estimation, such as the pattern and scale of dispersion of single-grain De values and dose rates, the associated measurement uncertainties, the effect of natural variability among grains, and the outlier probabilities of De and dose rate estimates. Here we propose an empirical Bayesian hierarchical age model (BHAM) for optical dating of quartz samples that incorporates the above information to estimate their depositional ages. The BHAM is based on the implementation of standardised growth curve and LnTn methods to integrate information on the full distribution of single-grain De values, sources of measurement uncertainty, beta-dose heterogeneity (observed or modelled), and detection of outliers. We present the results of validation tests using data sets of optically stimulated luminescence measurements and dose rates obtained for quartz samples dated previously from Denisova Cave (Russia) and for simulated samples. We conclude that the BHAM represents a robust and flexible approach to dealing with data for single grains of quartz within a Bayesian hierarchical framework and is suitable for application to sediments deposited in a variety of depositional settings.