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

Hydrological Processes

Volumn 25, Issue 18, 2011, Pages 2827-2836

  Trichakis, Ioannis ^a   Nikolos, Ioannis ^a   Karatzas, George P ^a  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

Author keywords

Artificial neural networks; Bootstrap; Confidence intervals; Karstic aquifers

Indexed keywords

BOOTSTRAP; BOOTSTRAP CONFIDENCE INTERVAL; BOOTSTRAP METHOD; CONFIDENCE INTERVAL; DATA SUBSETS; HYDRAULIC HEADS; KARSTIC AQUIFER; METEOROLOGICAL PARAMETERS; OBSERVATION WELLS; WORK SUPPORT;

AQUIFERS; FINANCIAL DATA PROCESSING; HYDROGEOLOGY;

NEURAL NETWORKS;

AQUIFER; ARTIFICIAL NEURAL NETWORK; BOOTSTRAPPING; CONFIDENCE INTERVAL; HYDROLOGY; NUMERICAL MODEL; RELIABILITY ANALYSIS;

EID: 80051598326     PISSN: 08856087     EISSN: 10991085     Source Type: Journal    
DOI: 10.1002/hyp.8044     Document Type: Article

References (52)

1. Abel U, Berger J. 1986. Comparison of Resubstitution, Data Splitting, the Bootstrap, and the Jackknife as Methods for Estimating Validity Indexes of New Marker Tests-a Monte-Carlo Study. Biometrical Journal 28: 899-908.
2. Aitkenhead MJ, Cooper RJ. 2008. Neural network time series prediction of environmental variables in a small upland headwater in NE Scotland. Hydrological Processes 22: 3091-3101.
3. Aqil M, Kita I, Yano A, Nishiyama S. 2007. Neural Networks for Real Time Catchment Flow Modeling and Prediction. Water Resources Management 21: 1781-1796.
4. Babu GJ, Feigelson ED. 1996. Astrostatistics. Chapman & Hall: New York; 12, p. 221.
5. Beven K. 2006. On undermining the science? Hydrological Processes 20: 3141-3146.
6. Beven K. 2008. On doing better hydrological science. Hydrological Processes 22: 3549-3553.
7. Bickel PJ, Freedman DA. 1981. Some Asymptotic Theory for the Bootstrap. Annals of Statistics 9: 1196-1217.
8. Bolle RM, Ratha NK, Pankanti S. 2004. Error analysis of pattern recognition systems-the subsets bootstrap. Computer Vision and Image Understanding 93: 1-33.
9. Brey T. 1990. Confidence-Limits for Secondary Production Estimates-Application of the Bootstrap to the Increment Summation Method. Marine Biology 106: 503-508.
10. Carpenter J. 1999. Test inversion bootstrap confidence intervals. Journal of the Royal Statistical Society Series B-Statistical Methodology 61: 159-172.
11. Cawley GC, Janacek GJ, Haylock MR, Dorling SR. 2007. Predictive uncertainty in environmental modelling. Neural Networks 20: 537-549.
12. Chernick MR. 2008. Bootstrap methods: a guide for practitioners and researchers. Wiley-Interscience: Hoboken, N.J.; 18, p. 369.
13. Chernick MR, Murthy VK, Nealy CD. 1985. Application of Bootstrap and Other Resampling Techniques-Evaluation of Classifier Performance. Pattern Recognition Letters 3: 167-178.
14. Chrysikopoulos CV, Hsuan P-Y, Fyrillas MM. 2002. Bootstrap estimation of the mass transfer coefficient of a dissolving nonaqueous phase liquid pool in porous media. Water Resources Research 38: 1026.
15. Chryssolouris G, Lee M, Ramsey A. 1996. Confidence interval prediction for neural network models. Ieee Transactions on Neural Networks 7: 229-232.
16. Cooley RL. 1997. Confidence intervals for ground-water models using linearization, likelihood, and bootstrap methods. Ground Water 35: 869-880.
17. Coppola EA, Rana AJ, Poulton MM, Szidarovszky F, Uhl VW. 2005. A neural network model for predicting aquifer water level elevations. Ground Water 43: 231-241.
18. da Silva RR, Siqueira MHS, de Souza MPV, Rebello JMA, Caloba LP. 2005. Estimated accuracy of classification of defects detected in welded joints by radiographic tests. Ndt & E International 38: 335-343.
19. Diaconis P, Efron B. 1983. Computer-Intensive Methods in Statistics. Scientific American 248: 116.
20. Efron B. 1979. 1977 Rietz Lecture-Bootstrap Methods-Another Look at the Jackknife. Annals of.
21. Efron B. 1988. Bootstrap Confidence-Intervals-Good or Bad. Psychological Bulletin 104: 293-296.
22. Efron B. 2003. Second thoughts on the bootstrap. Statistical Science 18: 135-140; Statistics 7: 1-26.
23. Efron B, Tibshirani R. 1993. An Introduction to the Bootstrap. Chapman & Hall: New York.
24. Egmont-Petersen M, Feelders A, Baesens B. 2005. Confidence intervals for probabilistic network classifiers. Computational Statistics & Data Analysis 49: 998-1019.
25. Ferrari SLP, Cribari-Neto F. 1998. On bootstrap and analytical bias corrections. Economics Letters 58: 7-15.
26. Ferrari SLP, Cribari-Neto F. 1999. On the robustness of analytical and bootstrap corrections to score tests in regression models. Journal of Statistical Computation and Simulation 64: 177-191.
27. Karterakis SM, Karatzas GP, Nikolos IK, Papadopoulou MP. 2007. Application of linear programming and differential evolutionary optimization methodologies for the solution of coastal subsurface water management problems subject to environmental criteria. Journal of Hydrology 342: 270-282.
28. Kisi O. 2007. Evapotranspiration modelling from climatic data using a neural computing technique. Hydrological Processes 21: 1925-1934.
29. Kisi O. 2008. The potential of different ANN techniques in evapotranspiration modelling. Hydrological Processes 22: 2449-2460.
30. Krishna B, Satyaji RYR, Vijaya T. 2008. Modelling groundwater levels in an urban coastal aquifer using artificial neural networks. Hydrological Processes 22: 1180-1188.
31. Lallahem S, Mania J. 2003. Evaluation and forecasting of daily groundwater outflow in a small chalky watershed. Hydrological Processes 17: 1561-1577.
32. Lallahem S, Mania J, Hani A, Najjar Y. 2005. On the use of neural networks to evaluate groundwater levels in fractured media. Journal of Hydrology 307: 92-111.
33. Maier HR, Dandy GC. 2000. Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environmental Modelling and Software 15: 101-124.
34. Masumoto K. 2003. Prediction error of groundwater behavior by inverse modeling with bootstrap re-sampling method. In Groundwater Engineering-Recent Advances, Komatsu M, Nishigaki M, Kono I (eds). Taylor & Francis; 579-584.
35. Mougiakakou SG, Valavanis IK, Nikita A, Nikita KS. 2007. Differential diagnosis of CT focal liver lesions using texture features, feature selectéon and ensemble driven classifiers. Artificial Intelligence in Medicine 41: 25-37.
36. Nayak P, Rao Y, Sudheer K. 2006. Groundwater Level Forecasting in a Shallow Aquifer Using Artificial Neural Network Approach. Water Resources Management 20: 77-90.
37. Nikolos IK, Stergiadi M, Papadopoulou MP, Karatzas GP. 2008. Artificial neural networks as an alternative approach to groundwater numerical modelling and environmental design. Hydrological Processes 22: 3337-3348.
38. Papadopoõlos G, Edwards PJ, Murray AF. 2001. Confidence estimation methods for neural networks: A practical comparison. Ieee Transactions on Neural Networks 12: 1278-1287.
39. Rivals I, Personnaz L. 2000. Construction of confidence intervals for neural networks based on least squares estimation. Neural Networks 13: 463-484.
40. Samani N, Gohari-Moghadam M, Safavi AA. 2007. A simple neural network model for the determination of aquifer parameters. Journal of Hydrology 340: 1-11.
41. Schervish MJ. 1995. Theory of statistics. Springer-Verlag: New York; 16, p. 702.
42. Silva RR, Mery D. 2007. Accuracy estimation of detection of casting defects in X-ray images using some statistical techniques. Insight 49: 603-609.
43. Singh K. 1981. On the Asymptotic Accuracy of Efrons Bootstrap. Annals of Statistics 9: 1187-1195.
44. Szidarovszky F, Coppola Jr. EA, Long J, Hall AD, Poulton MM. 2007. A hybrid artificial neural network-numerical model for ground water problems. Ground Water 45: 590-600.
45. Terzic J, Sumanovac F, Buljan R. 2007. An assessment of hydrogeological parameters on the karstic island of Dugi Otok, Croatia. Journal of Hydrology 343: 29-42.
46. Thomas SH, Padilla-Crespo E, Jardine PM, Sanford RA, Loffler FE. 2009. Diversity and Distribution of Anaeromyxobacter Strains in a Uranium-Contaminated Subsurface Environment with a Nonuniform Groundwater Flow. Applied and Environmental Microbiology 75: 3679-3687.
47. Todini E, Mantovan P. 2007. Comment on: 'On undermining the science?' by Keith Beven. Hydrological Processes 21: 1633-1638.
48. Trichakis IC, Nikolos IK, Karatzas GP. 2009. Optimal selection of artificial neural network parameters for the prediction of a karstic aquifer's response. Hydrological Processes 23: 2956-2969.
49. Tsujitani M, Sakon M. 2009. Analysis of Survival Data Having Time-Dependent Covariates. Ieee Transactions on Neural Networks 20: 389-394.
50. Varol Y, Avci E, Koca A, Oztop HF. 2007. Prediction of flow fields and temperature distributions due to natural convection in a triangular enclosure using Adaptive-Network-Based Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN). International Communications in Heat and Mass Transfer 34: 887-896.
51. Wahrendorf J, Brown CC. 1980. Bootstrapping a Basic Inequality in the Analysis of Joint Action of 2 Drugs. Biometrics 36: 653-657.
52. White H, Racine J. 2001. Statistical inference, the bootstrap, and neural-network modelling with application to foreign exchange rates. IEEE Transactions on Neural Networks 12: 657-673.