Comparison of bootstrap confidence intervals for an ANN model of a karstic aquifer response

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Following many applications artificial neural networks (ANNs) have found in hydrology, a question has been rising for quantification of the output uncertainty. A pre-optimized ANN simulated the hydraulic head change at two observation wells, having as input hydrological and meteorological parameters. In order to calculate confidence intervals (CI) for the ANN output two bootstrap methods were examined namely bootstrap percentile and BCa (Bias-Corrected and accelerated). The actual coverage of the CI was compared to the theoretical coverage for different certainty levels as a means of examining the method's reliability. The results of this work support the idea that the bootstrap methods provide a simple tool for confidence interval computation of ANNs. Comparing the two methods, the percentile requires fewer calculations and yields narrower intervals with similar actual coverage to that of BCa. Overall, the actual coverage was proved lower than desired when not modeled points were present in the data subset. Copyright © 2011 John Wiley & Sons, Ltd.

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