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Sensitivity analysis of kernel estimates: implications in nonlinear physiological system identification

D T Westwick1, B Suki, K R Lutchen

  • 1Department of Biomedical Engineering, Boston University, MA 02215, USA. westwick@bu.edu

Annals of Biomedical Engineering
|May 7, 1998
PubMed
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This study introduces a new method to estimate the reliability of nonlinear system kernels from single data records. This approach provides confidence bounds for kernel estimates and output predictions, validated in auditory system models.

Area of Science:

  • Nonlinear system identification
  • Biomedical engineering
  • Signal processing

Background:

  • Volterra/Wiener kernels are crucial for nonlinear system analysis, especially in physiology.
  • Existing methods lack reliability estimation from single data records.

Purpose of the Study:

  • To develop a formal analysis of variance for least-squares nonlinear system identification.
  • To enable reliability estimation and confidence bounds for kernel coefficients and predictions from single data records.

Main Methods:

  • Developed formal analysis of variance for least-squares nonlinear system identification algorithms.
  • Derived expressions for the variance of estimated kernel coefficients.
  • Applied confidence bounds to Korenberg's fast orthogonal algorithm and the Laguerre expansion technique.

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Main Results:

  • Theoretical derivations were validated using simulations of a peripheral auditory system model.
  • Demonstrated excellent agreement between single-trial and ensemble-averaged variance estimates.
  • Validated techniques with various input signals and output noise conditions.

Conclusions:

  • The developed methods provide reliable confidence bounds for nonlinear system kernel estimates from single data records.
  • This advancement is significant for analyzing physiological systems and other complex nonlinear systems.
  • The approach is robust to different input types and independent output noise characteristics.