Bayesian analysis of De distributions in optical dating: Towards a robust method for dealing with outliers

In optical dating, especially single-grain dating, various patterns of distributions in equivalent dose (D_e) are usually observed and analysed using different statistical models. None of these methods, however, is designed to deal with outliers that do not form part of the population of grains associated with the event of interest (the ‘target population’), despite outliers being commonly present in single-grain D_e distributions. In this paper, we present a Bayesian method for detecting D_e outliers and making allowance for them when estimating the D_e value of the target population. We test this so-called Bayesian outlier model (BOM) using data sets obtained for individual grains of quartz from sediments deposited in a variety of settings, and in simulations. We find that the BOM is suitable for single-grain D_e distributions containing outliers that, for a variety of reasons, do not form part of the target population. For example, D_e outliers may be associated with grains that have undesirable luminescence properties (e.g., thermal instability, high rates of anomalous fading) or with contaminant grains incorporated into a sample when collected in the field or prepared in the laboratory. Grains that have much larger or smaller D_e values than the target population, due to factors such as insufficient bleaching, beta-dose heterogeneity or post-depositional disturbance, may also be identified as outliers using the BOM, enabling these values to be weighted appropriately for final D_e and age determination.