A Bayesian hierarchical age model for single-grain optical dating of feldspars

The distribution of equivalent dose (D_e) values of individual feldspar grains is affected by a range of variables, including internal and external dose rates, residual doses, and uncertainties associated with luminescence behaviours and measurement errors. The distributions of these variables may be non-Gaussian, resulting in a complex D_e distribution pattern that may be challenging to interpret and analyse using conventional statistical models. To address this problem, we present an empirical Bayesian hierarchical age model for feldspar (BHAM-F), which integrates all key components involved in the optical dating of individual feldspar grains. The model is based on application of the standardised growth curve and L_nT_n methods to obtain a full distribution of single-grain D_e values, and use of prior information about major sources of uncertainty that can be obtained experimentally or theoretically. A Bayesian outlier model is also adopted to detect and deal with outliers. We test and validate the BHAM-F using an experimentally gathered dataset obtained from a sediment sample and various simulated datasets. Our results show that the BHAM-F provides a robust and flexible way to hierarchically deal with data obtained in single-grain optical dating of feldspars.