Luminescence age calculation through Bayesian convolution of equivalent dose and dose-rate distributions: the D_e_D_r model

In nature, any mineral grain (quartz or feldspar) receives a dose-rate (Dr) specific to its environment. The dose-rate distributions, therefore, reflect the micro-dosimetric context of grains of similar size. If all the grains have been well bleached at deposition, this distribution corresponds, within uncertainties, to the distribution of equivalent doses (De). Their combination (convolution of the De and Dr distributions in the De_Dr model proposed here) allows the calculation of the true depositional age. If grains whose De values are not representative of this age (hereafter called "outliers") are present in the De distribution, the model allows them to be identified before the age is calculated. As the De_Dr approach relies only on the Dr distribution, the model avoids any assumption representing the De distribution, which is usually difficult to justify. Herein, we outline the mathematical concepts of the De_Dr approach (more details are given in Galharret et al., accepted) and the exploitation of this Bayesian modelling based on an R code available in the R package 'Luminescence'. We also present a series of tests using simulated Dr and De distributions with and without outliers and show that the De_Dr approach can be an alternative to available models for interpreting De distributions.