Abstract
The research towards improving the prediction and forecasting of artificial neural network (ANN) based models has gained significant interest while solving various engineering problems. Consequently, different approaches for the development of ANN models have been proposed. However, the point estimation of ANN forecasts seldom explains the actual mechanism that brings the relationship among modeled variables. This raises the question on the model output while making decisions due to the inherent variability or uncertainty associated. The standard procedure though available for the quantification of uncertainty, their applications in ANN model are still limited. In this chapter, commonly employed uncertainty methods such as bootstrap and Bayesian are applied in ANN and demonstrated through a case example of flood forecasting models. It also discusses the merits and limitations of bootstrap ANN (BTANN) and Bayesian ANN (BANN) models in terms of convergence of parameter and quality of prediction interval evaluated using uncertainty indices.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K.P. Sudheer, Knowledge extraction from trained neural network river flow models. J. Hydrol. Eng. 10(4), 264–269 (2005)
H.R. Maier, A. Jain, G.C. Dandy, K.P. Sudheer, Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ. Model Softw. 25, 891–909 (2010)
A. Elshorbagy, G. Corzo, S. Srinivasulu, D.P. Solomatine, Experimental investigation of the predictive capabilities of data driven modeling techniques in hydrology—Part 2: concepts and methodology. Hydrol. Earth Syst. Sci. 14(10), 1931–1941 (2010)
A. Elshorbagy, G. Corzo, S. Srinivasulu, D.P. Solomatine, Experimental investigation of the predictive capabilities of data driven modeling techniques in hydrology—Part 2: application. Hydrol. Earth Syst. Sci. 14(10), 1943–1961 (2010)
C.M. Bishop, Neural Networks for Pattern Recognition (Oxford University Press, New York, 1995)
D.L. Shrestha, D.P. Solomatine, Machine learning approaches for estimation of prediction interval for the model output. Neural Netw. 19, 225–235 (2006)
T. Wagener, H.V. Gupta, Model identification for hydrological forecasting under uncertainty. Stoch. Environ. Res. Risk Assess. 19(6), 378–387 (2005)
K.J.C. MacKay, A practical Bayesian framework for backpropagation. Netw. Neural Comput. 4, 448–472 (1992)
N.M. Radford, Bayesian Learning for Neural Networks. Lecture Notes in Statistics, vol. 118 (Springer, NewYork, (1996)
M.S. Khan, P. Coulibaly, Y. Dibike, Uncertainty analysis of statistical downscaling methods. J. Hydrol. 319, 357–382 (2006)
X. Zhang, F. Liang, R. Srinivasan, M. Van Liew, Estimating uncertainty of streamflow simulation using Bayesian neural networks. Water Resour. Res. 45(2), 1–16 (2009)
R.K. Srivastav, K.P. Sudheer, I. Chaubey, A simplified approach to quantifying predictive and parametric uncertainty in artificial neural network hydrologic models. Water Resour. Res. 43(10), W10407 (2007)
S.K. Sharma, K.N. Tiwari, Bootstrap based artificial neural network (BANN) analysis for hierarchical prediction of monthly runoff in Upper Damodar Valley Catchment. J. Hydrol. 374(3–4), 209–222 (2009)
R.R. Shrestha, F. Nestmann, Physically Based and data-driven models and propagation of Input uncertainties in river flood prediction. J. Hydrol. Eng. 14(December), 1309–1319 (2009)
S. Alvisi, M. Franchini, Fuzzy neural networks for water level and discharge forecasting with uncertainty. Environ. Model Softw. 26(4), 523–537 (2011)
G.J. Bowden, H.R. Maier, G.C. Dandy, Input determination for neural network models in water resources applications. Part 1—background and methodology. J. Hydrol. 301(1–4), 75–92 (2005)
G.J. Bowden, H.R. Maier, G.C. Dandy, Input determination for neural network models in water resources applications. Part 2—case study: forecasting salinity in a river. J. Hydrol. 301(1–4), 93–107 (2005)
M. Campolo, A. Soldati, P. Andreussi, Forecasting river flow rate during low-flow periods using neural networks. Water Resour. Res. 35(11), 3547–3552 (1999)
K. Thirumalaiah, M.C. Deo, Hydrological forecasting using neural networks. J. Hydrol. Eng. 5(2), 180–189 (2000)
D. Silverman, J.A. Dracup, Artificial neural networks and long-range precipitation in California. J. Appl. Meteorol. 31(1), 57–66 (2000)
K.P. Sudheer, A.K. Gosain, K.S. Ramasastri, A data-driven algorithm for constructing artificial neural network rainfall-runoff models. Hydrol. Process. 16(6), 1325–1330 (2002)
A.S. Tokar, P.A. Johnson, Rainfall-runoff modeling using artificial neural networks. J. Hydrol. Eng. 4(3), 232–239 (1999)
B. Efron, Bootstrap methods: another look at jackknife. Ann. Stat. 7(1), 26 (1979)
A.P. Piotrowski, J.J. Napiorkowski, A comparison of methods to avoid overfitting in neural networks training in the case of catchment runoff modelling. J. Hydrol. 476, 97–111 (2013)
R.J. Abrahart, L. See, Comparing neural network and autoregressive moving average techniques for the provision of continuous river flow forecasts in two contrasting catchments. Hydrol. Process. 14(11–12), 2157–2172 (2000)
P.C. Nayak, K.P. Sudheer, D.M. Rangan, K.S. Ramasastri, Short-term flood forecasting with a neurofuzzy model. Water Resour. Res. 41(4), 1–16 (2005). December 2004
K.S. Kasiviswanathan, R. Cibin, K.P. Sudheer, I. Chaubey, Constructing prediction interval for artificial neural network rainfall runoff models based on ensemble simulations. J. Hydrol. 499, 275–288 (2013)
J.E. Nash, J.V. Sutcliffe, River flow forecasting through conceptual models: 1. A discussion of principles. J. Hydrol. 10, 282–290 (1970)
K.S. Kasiviswanathan, K.P. Sudheer, Quantification of the predictive uncertainty of artificial neural network based river flow forecast models. Stoch. Environ. Res. Risk Assess. 27(1), 137–146 (2013)
M. Chetan, K.P. Sudheer, A hybrid linear-neural model for river flow forecasting. Water Resour. Res. 42, W04402 (2006). doi:10.1029/2005WR004072
M.K. Tiwari, J. Adamowski, Urban water demand forecasting and uncertainty assessment using ensemble wavelet-bootstrap-neural network models. Water Resour. Res. 49(10), 6486–6507 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kasiviswanathan, K.S., Sudheer, K.P., He, J. (2016). Quantification of Prediction Uncertainty in Artificial Neural Network Models. In: Shanmuganathan, S., Samarasinghe, S. (eds) Artificial Neural Network Modelling. Studies in Computational Intelligence, vol 628. Springer, Cham. https://doi.org/10.1007/978-3-319-28495-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-28495-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28493-4
Online ISBN: 978-3-319-28495-8
eBook Packages: EngineeringEngineering (R0)