BEMMA: A Hierarchical Bayesian End-Member Modeling Analysis of Sediment Grain-Size Distributions

Abstract

Sediment grain-size distributions provide rich information about sedimen- tary dynamics and potentially about environmental and climatic changes. However, entrainment, transport, and deposition, as a sequence of sorting process, modify original grain-size distributions of source materials, thereby resulting in complex distribution forms that are commonly multimodal and asymmetrical. However, nei- ther traditional descriptive statistics nor curving fitting methods are able to address this complexity fully. End-member modeling analysis, essentially based on polytope expansion, stands out as a flexible and robust method for the unmixing of sediment grain-size distributions. Yet there are still several key issues that remain unresolved. Here a hierarchical Bayesian end-member modeling analysis of grain-size distribu- tions, fully subject to the non-negative and unit-sum constraints on the distributions, is presented. Within the Bayesian framework, the number of end members, as well as the end-member spectra and fractions can be inferred sequentially using a reversible- jump Markov chain Monte Carlo algorithm in conjunction with Gibbs samplers. Test runs using both a synthetic and a real-world dataset from a small playa located on the southern margin of the Badain Jaran Desert, NW China, reveal that this model