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 parameterises 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 Coutts et 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.

在该杂志最近发表的评论中，Coutts等人。（2019）比较了九种通过碎屑年代学估算硅质岩最大沉积年龄（MDA）的方法。他们的结果表明，在这些方法中，有3种是正偏的，而6种是负偏的。本文研究了造成这些偏差的原因，并提出了解决方案。一个简单的玩具示例表明，从理论上讲，即使是在最理想的情况下，所审查的方法也无法找到正确的沉积年龄：MDA估计随着样本量的增加，漂移会变得越来越小。可以使用最大可能性模型解决该问题，该模型最初是由Galbraith和Laslett（1993）为裂变径迹年代学开发的。这种方法通过离散和连续分布的二元混合参数化了MDA估计问题。与Coutts等人审查的临时方法不同，“最大可能年龄”（MLA）算法收敛于唯一的MDA值。（2019）。它成功地恢复了玩具实例的沉积年龄，并为实际分布产生了合理的结果。公开发布的13个砂岩样品数据集的应用对此进行了说明，该样品已通过LA-ICPMS和CA-TIMS U–Pb地质年代学进行了分析。临时算法会产生不切实际的MDA估计值，相对于CA-TIMS数据，LA-ICPMS数据在系统上要年轻得多。MLA算法不受此负偏差的影响。MLA方法是用于MDA估计的纯统计方法。就像临时方法一样 它不能轻易地适应地质问题，例如沉积后的Pb损失，或导致错误的年轻异常值的分析问题。在这种复杂情况下，最好的方法是使用更精确的测年技术重新分析最年轻的谷物。MLA方法的结果最好在径向图上可视化。模型和标绘图都可以在碎屑年代学之外应用，例如确定火山喷发年龄。