Bayesian model selection applied to artificial neural networks used for water resources modeling

Artificial neural networks (ANNs) have proven to be extremely valuable tools in the field of water resources engineering. However, one of the most difficult tasks in developing an ANN is determining the optimum level of complexity required to model a given problem, as there is no formal systematic model selection method. 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 Markov Chain Monte Carlo 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 suitability for being incorporated into the proposed BMS framework for ANNs. However, it is acknowledged that it can be particularly difficult to accurately estimate the evidence of ANN models. 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 unambiguously indicate any redundancies in the hidden layer nodes. 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 advantages of a total Bayesian approach to ANN development, including training and model selection, are demonstrated on two synthetic and one real world water resources case study.Kingston, G. B., H. R. Maier, and M. F. Lamber

Optimal division of data for neural network models in water resources applications

The way that available data are divided into training, testing, and validation subsets can have a significant influence on the performance of an artificial neural network (ANN). Despite numerous studies, no systematic approach has been developed for the optimal division of data for ANN models. This paper presents two methodologies for dividing data into representative subsets, namely, a genetic algorithm (GA) and a self-organizing map (SOM). These two methods are compared with the conventional approach commonly used in the literature, which involves an arbitrary division of the data. A case study is presented in which ANN models developed using each data division technique are used to forecast salinity in the River Murray at Murray Bridge (South Australia) 14 days in advance. When tested on a validation data set from July 1992 to March 1998, the models developed using the GA and SOM data division techniques resulted in a reduction in RMS error of 24.2% and 9.9%, respectively, over the conventional data division method. It was found that a SOM could be used to diagnose why an ANN model has performed poorly, given that the poor performance is primarily related to the data themselves and not the choice of the ANN's parameters or architecture.Gavin J. Bowden, Holger R. Maier and Graeme C. Dand

Fuzzy exemplar-based inference system for flood forecasting

[[abstract]][1] Fuzzy inference systems have been successfully applied in numerous fields since they can effectively model human knowledge and adaptively make decision processes. In this paper we present an innovative fuzzy exemplar-based inference system (FEIS) for flood forecasting. The FEIS is based on a fuzzy inference system, with its clustering ability enhanced through the Exemplar-Aided Constructor of Hyper-rectangles algorithm, which can effectively simulate human intelligence by learning from experience. The FEIS exhibits three important properties: knowledge extraction from numerical data, knowledge (rule) modeling, and fuzzy reasoning processes. The proposed model is employed to predict streamflow 1 hour ahead during flood events in the Lan-Yang River, Taiwan. For the purpose of comparison the back propagation neural network (BPNN) is also performed. The results show that the FEIS model performs better than the BPNN. The FEIS provides a great learning ability, robustness, and high predictive accuracy for flood forecasting.[[notice]]補正完畢[[incitationindex]]SCI[[incitationindex]]E