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Confidence intervals for calibration with neural networks

Abstract

Based on neural network calibration the confidence intervals of aromaticity determination from infrared reflectance spectra of raw brown coals were estimated by means of the bootstrap method, a simplified Monte Carlo Simulation. The standard deviations and the confidence intervals were estimated to characterise the analysis error. It is shown that confidence intervals of non-linear analysis methods like Back Propagation Neural Networks (BPNN) can be estimated by the bootstrap method. The estimated confidence intervals of the calibration confirm the analysis by BPNN.

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References

  1. Næs T (1992) Progress in multi-variate calibration. In: Hildrum I, Isaksson T, Næs T, Tandberg A (eds) Near infra-red spectroscopy. Ellis Horwood, New York, pt 3, ch 8, pp 51–60

    Google Scholar 

  2. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1986, 1992) Numerical recipes in FORTRAN. University Press, Cambridge

    Google Scholar 

  3. Baxt WG, White H (1995) Neural Comput 7: 3: 624–638

    Article  CAS  Google Scholar 

  4. Rumelhart DE, Hinton GE, Williams RJ (1986) Parallel distributed processing, vol. 1. MIT Press, Cambridge, p 318

    Google Scholar 

  5. Zupan J, Gasteiger J (1993) Neural networks for chemists. VCH, Weinheim

    Google Scholar 

  6. Zupan J, Gasteiger J (1991) Anal Chim Acta 248: 1–30

    Article  CAS  Google Scholar 

  7. Dathe M (1992) Neuronale Netze für die Mehrkomponenten-analyse. Diplomarbeit, TU Bergakademie Freiberg

  8. Massart DL, Vandeginste BGM, Deming SN, Michotte Y, Kaufman L (1988, 1990) Chemometrics: a textbook. Elsevier, Amsterdam

    Google Scholar 

  9. Schierle C, Otto M (1992) Fresenius J Anal Chem 344: 190–194

    Article  CAS  Google Scholar 

  10. Efron B, Stein C (1981) Ann Statist 1: 3: 586–596

    Article  Google Scholar 

  11. Efron B (1979) Ann Statist 7: 1: 1–26

    Article  Google Scholar 

  12. Doerffel K (1987) Statistik in der analytischen Chemie. VCH, Weinheim

    Google Scholar 

  13. Tesch S (1992) Kohlecharakterisierung auf der Grundlage in-frarotspektroskopischer Mehrkomponentenanalysen. Dissertation, TU Bergakademie Freiberg

  14. Zupan J (1989) Algorithms for chemists. Wiley, New York

    Google Scholar 

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Dathe, M., Otto, M. Confidence intervals for calibration with neural networks. Fresenius J Anal Chem 356, 17–20 (1996). https://doi.org/10.1007/s0021663560017

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  • DOI: https://doi.org/10.1007/s0021663560017

Keywords

  • Bootstrap Method
  • Brown Coal
  • Back Propagation Neural Network
  • Estimate Confidence Interval
  • Computing Workload