Application of the Bayesian approach to sediment fingerprinting and source attribution

The identification of the sources of sediment is a key part of the management of waterways. This is typically achieved through the well-established technique known as sediment source fingerprinting that uses tracers and statistical mixing models. Until recently, the approach for solving these mixing models has been dominated by frequentist methods. This review focuses on the growing interest in Bayesian methods for sediment fingerprinting and presents them as an alternative or complementary addition to the frequentist methods. Bayesian methods emphasize flexibility, for example, in the choice of probability distributions for tracers, inclusion of parameter probability terms, the choice of how to characterize tracer proportion, and the choice of fully or empirical Bayesian techniques. The Bayesian approach flexibly combines previous known and current information, to produce results that aim to accurately reflect the real-world environment. Under the Bayesian paradigm, all model parameters are treated as random variables, and this allows all sources of variation to be explicitly communicated and modelled. Although there are considerable advantages to using a Bayesian approach for sediment tracing, there are some possible problems the practitioner should be aware of. These include computational issues and potential difficulties in choosing probability distributions to realistically represent model parameters. Though there are choices as to what Bayesian approach to implement (i.e., fully or empirical Bayesian), a fully Bayesian approach has been found to best retain fidelity to the Bayesian paradigm of treating all parameters as random variables. It has been recognized that the field of sediment source fingerprinting would greatly benefit from the development of a model that incorporates the tracer selection process into the modelling framework allowing for an all-in-one approach, and the flexibility of a Bayesian approach makes this development possible.