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

Abstract

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. • A Bayesian outlier model (BOM) for luminescence dating of sediments. • Outliers are identified in single-grain equivalent dose (D e ) distributions. • Outliers are weighted appropriately for final D e and age determination. • Three special cases (BOM central, minimum and maximum) for different contexts. • Tested on well-bleached, partially bleached and post-depositionally mixed samples.