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Type: Journal article
Title: Bayesian model selection applied to artificial neural networks used for water resources modeling
Author: Humphrey, G.
Maier, H.
Lambert, M.
Citation: Water Resources Research, 2008; 44(4):04419-01-04419-12
Publisher: Amer Geophysical Union
Issue Date: 2008
ISSN: 0043-1397
Statement of
Kingston, G. B., H. R. Maier, and M. F. Lambert
Abstract: 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.
Keywords: artificial neural networks
water resources modeling
Bayesian model selection
Markov chain Monte Carlo
evidence estimation
Rights: Copyright 2008 by the American Geophysical Union
DOI: 10.1029/2007WR006155
Appears in Collections:Aurora harvest
Civil and Environmental Engineering publications
Environment Institute publications

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