The hydrologist's guide to Bayesian model selection, averaging and combination

Model selection and model averaging have become popular tools to address conceptual uncertainty in hydro (geo)logical modeling. Within the last two decades, many different flavors of approaches and implementations have emerged which complicate an easy access to and a thorough understanding of the underlying principles. With the many approaches and applications, a variety of terms has been defined, which easily leads to misunderstandings and confusion among the community. Here, we review Bayesian model selection (BMS) and averaging (BMA) as a rigorous statistical framework for model choice under uncertainty. We aim to clarify the theoretical foundations of both methods, their relationship to one another and to alternative approaches, and implications of implementation choices. We further build a bridge to Bayesian model combination (BMC) which turns out to be Bayesian averaging or selection of combined models (BCMA/BCMS). Concluding from our theoretical review, we argue that the goal and the philosophical perspective of modeling should be main drivers when choosing to use the B(C)MS/A toolbox, and we offer guidance to identify the suitable approach for specific modeling goals. With this review, we hope to further strengthen the utility of Bayesian methods in the face of conceptual uncertainty by directing their use into the right channels.