Maximum depositional age estimation revisited

In a recent review published in this journal, Coutts et al. (2019) compared nine different ways to estimate the maximum depositional age (MDA) of siliclastic rocks by means of detrital geochronology. Their results show that among these methods three are positively and six negatively biased. This paper investigates the cause of these biases and proposes a solution to it. A simple toy example shows that it is theoretically impossible for the reviewed methods to find the correct depositional age in even a best case scenario: the MDA estimates drift to ever smaller values with increasing sample size. The issue can be solved using a maximum likelihood model that was originally developed for fission track thermochronology by Galbraith and Laslett (1993). This approach param- eterises the MDA estimation problem with a binary mixture of discrete and continuous distributions. The `Maximum Likelihood Age' (MLA) algorithm converges to a unique MDA value, unlike the ad hoc methods reviewed by Courts a al. (2019). It successfully recovers the depositional age for the toy example, and produces sensible results for realistic distributions. This is illustrated with an application to a published dataset of 13 sandstone samples that were analysed by both LA-ICPMS and CA-TIMS U-Pb geochronology. The ad hoc algorithms produce unrealistic MDA estimates that are systematically younger for the LA-ICPMS data than for the CA-TIMS data. The MLA algorithm does not suffer from this negative bias. The MLA method is a purely statistical approach to MDA estimation. Like the ad hoc methods, it does not readily accommodate geological complications such as post-depositional Pb-loss, or analytical issues causing erroneously young outliers. The best approach in such complex cases is to re-analyse the youngest grains using more accurate dating techniques. The results of the MLA method are best visualised on radial plots. Both the model and the plots have applications outside detrital geochronology, for example to determine volcanic eruption ages.