Sedimentary deposits constitute the primary record of changing environmental conditions that have acted on Earth’s surface over geologic time. Clastic material is eroded from source locations (parents) in sediment routing systems and deposited at sink locations (children). Both parents and children have characteristics that vary across many different dimensions, including grain size, chemical composition, and the geochronologic age of constituent detrital minerals. During transport, sediment from different parents is mixed together to form a child, which in turn may serve as the parent for other sediment farther down-system or later in time when buried sediment is exhumed. The distribution of detrital mineral ages observed in parent and child sediments allows for investigation of the proportion of each parent in the child sediment, which reflects the properties of the sediment routing system. To model the proportion of dates in a child sample that comes from each of the parent distributions, we use a Bayesian mixture of Dirichlet processes. This model enables us to estimate the mixing proportions with associated uncertainty while making minimal assumptions. We also present an extension to the model whereby we reconstruct unobserved parent distributions from multiple observed child distributions using mixtures of Dirichlet processes. The model accounts for uncertainty in both the number of mineral formation events that constitute each parent distribution and the mixing proportions of each parent distribution that constitutes a child distribution. To demonstrate the model, we perform analyses using simulated data where the true age distribution is known as well as using a real-world case study from the coast of central California, USA.

沉积物是地质时期作用于地球表面的环境条件变化的主要记录。碎屑材料从沉积物路径系统中的源位置（母体）被侵蚀并沉积在汇位置（子体）。父母和孩子都具有在许多不同维度上变化的特征，包括颗粒大小、化学成分和组成碎屑矿物的地质年代。在运输过程中，来自不同母体的沉积物混合在一起形成一个子体，而子体又可以作为其他沉积物的母体，这些沉积物在系统更远的下游或在挖掘出埋藏的沉积物时稍后时间。在母体和子沉积物中观察到的碎屑矿物年龄分布允许调查每个母体在子沉积物中的比例，这反映了沉积物路径系统的特性。为了模拟来自每个父分布的子样本中日期的比例，我们使用 Dirichlet 过程的贝叶斯混合。该模型使我们能够在做出最小假设的同时估计具有相关不确定性的混合比例。我们还提出了对模型的扩展，我们使用 Dirichlet 过程的混合从多个观察到的子分布重建未观察到的父分布。该模型考虑了构成每个父分布的矿物形成事件数量和构成子分布的每个父分布的混合比例的不确定性。为了演示模型，