Selecting a conceptual hydrological model using Bayes' factors computed with replica exchange Hamiltonian Monte Carlo and thermodynamic integration

We develop a method for computing Bayes’ factors of conceptual rainfall-runoff models based on thermodynamic integration, gradient-based replica-exchange Markov Chain Monte Carlo algorithms and modern differentiable programming languages. We apply our approach to the problem of choosing from a set of conceptual bucket-type models with increasing dynamical complexity calibrated against both synthetically generated and real runoff data from Magela Creek, Australia. We show that using the proposed methodology the Bayes factor can be used to select a parsimonious model and can be computed robustly in a few hours on modern computing hardware. We introduce formal posterior predictive checks for the selected model. The prior calibrated posterior predictive p-value, which also tests for prior data conflict, is used for the posterior predictive checks. Prior data conflict is when the prior favours parameter values that are less likely given the data.