The chemical composition of sediments is controlled predominantly by the sediment grain size, and thus evaluating their relationship is an important task in sedimentary geochemistry. The grain size is characterized by the respective particle size distribution, which can be expressed as a probability density function. Because of the relative character of densities, the Bayes space methodology was employed to build a regression model between a real response and a density function as a covariate, here the chemical composition and the particle size density. For practical computations, density functions were expressed in the standard \(L^2\) space using the centred logratio transformation and spline approximation of the input discretized densities was utilized by respecting the induced zero-integral constraint. After a concise simulation study, supporting the relevance of the proposed regression model, the new methodology was applied to examine the relationship between sediment grain size and geochemical composition, with samples being obtained in the Czech Republic in the Skalka Reservoir and in the Ohře River floodplain upstream of the reservoir, to reveal proper grain size proxies. The Al/Si and Zr/Rb logratios in the sediments that were studied showed grain-size control, which makes them suitable for this purpose.

沉积物的化学组成主要受沉积物粒度控制，因此评估它们之间的关系是沉积地球化学中的重要任务。晶粒尺寸的特征在于各自的粒径分布，其可以表示为概率密度函数。由于密度的相对特性，采用贝叶斯空间方法在真实响应和作为协变量的密度函数（此处为化学成分和粒度密度）之间建立回归模型。对于实际计算，密度函数以标准\（L ^ 2 \）表示通过考虑诱导零积分约束，利用中心对数比变换和输入离散密度的样条近似来利用空间。经过简要的模拟研究，并支持了所建议的回归模型的相关性，该新方法被用于检验沉积物粒度与地球化学成分之间的关​​系，并在捷克共和国的Skalka水库和奥赫河泛滥区获得了样本在储层的上游，以揭示适当的粒度代理。研究的沉积物中的Al / Si和Zr / Rb对数比显示出晶粒尺寸控制，使其适合于此目的。