Bayesian model selection applied to artificial neural networks used for water resources modeling (original) (raw)

While artificial neural networks (ANNs) can be extremely valuable tools for water resources modeling, it is difficult to determine the optimum complexity required to model a given problem. This paper presents a Bayesian model selection (BMS) method for ANNs that provides an objective approach for comparing models of varying complexity in order to select the most appropriate ANN structure. The approach uses MCMC posterior simulations to estimate the evidence in favor of competing models and, in this study, three known methods for doing this are compared in terms of their accuracy and appropriateness for being incorporated into the proposed framework. However, it is acknowledged that evidence approximations based on posterior simulations may be sensitive to factors associated with the MCMC simulation. Therefore, the proposed BMS approach for ANNs incorporates a further check of the evidence results by inspecting the marginal posterior distributions of the hidden-to-output layer weights, which indicate whether all of the hidden nodes in the model are necessary. The fact that this check is available is one of the greatest advantages of the proposed approach over conventional model selection methods, which do not provide such a test and instead rely on the modeler's subjective choice of selection criterion. The proposed BMS approach is demonstrated on two synthetic and one real world water resources case study.