Luke Andrew Yates, Zach Aandahl, Barry W. Brook , Zenobia Jacobs, Bo Li, Bruno David

In applications of optically stimulated luminescence (OSL) dating to unconsolidated sediments, the burial age of a sample of grains is estimated using statistical models of the distribution of the experimentally determined equivalent doses of the grains, together with estimates of the environmental dose rate. For grains that have been vertically mixed after deposition (e.g., due to bioturbation), existing dose models may fail to appropriately account for the complexity of the mixing process, thus producing inaccurate age estimates of the original time of deposition of the `native' grains in any particular sample (usually the quantity of most interest). Here we introduce a new dose model, the asymmetric Laplacian mixture model (ALMM), developed for vertically mixed samples with single-grain dose distributions. The approach is based on a continuous statistical mixture that models the displacement of grains in both upward and downward directions. The central dose of the native grains in each sediment sample is estimated by the ALMM, as well as the parameters associated with overdispersion of single-grain dose distributions and the (modelled) mixing process. Using Bayesian methodology, we apply the model to two series of vertically contiguous samples collected at the site of Nawarla Gabarnmang in northern Australia. Independent age estimates obtained from radiocarbon dating of charcoal fragments support the OSL ages for the native grains estimated by the ALMM. Moreover, our study includes sensitivity analyses that show the model is robust to variation in the experimental error of the OSL data. The ALMM is introduced in the context of compound Gaussian distributions, a broadly encompassing statistical framework that includes many of the most commonly used dose models. This unifying and accessible perspective on the statistical modelling of dose distributions will support practitioners in selecting an appropriate model for samples affected by post-depositional mixing, and hopefully stimulate further theoretical developments. A new R rstanosl package is provided that fits the ALMM and other commonly used dose models using Hamiltonian Monte Carlo methods via the Stan programming language.