Traditional and Bayesian Statistical Models in Fluvial Sediment Transport

Abstract

The characterization of sediment transport is an important problem that has been actively studied for some time. Numerous approaches have been demonstrated in the literature, including mechanistic models, probabilistic arguments, machine learning algorithms, and empirical formulations. Most implementations of sediment transport relations are deterministic in nature and require the specification of model parameters. These parameters are traditionally assumed fixed (i.e., a single value), and subsequent predictions are not necessarily representative because of uncertainty because they are fixed (i.e., a line). In this paper, a Bayesian statistical sediment transport model is presented, and its ability to infer critical shear values from observations to nonlinear regression is compared. This approach provides several advantages, namely (1) parameters are not constrained to be normally distributed as is required in many traditional approaches; (2) estimates of parameter variability are easily obtained and interpreted from distributions that arise naturally from the estimation and prediction process; and (3) predictive distributions, or probability densities of predictions, are easily obtained through Bayesian methods and provide a robust way to sediment transport probabilistically centered on a deterministic formulation.