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Estimating Parameter Uncertainty in Binding-Energy Models by the Frequency-Domain Bootstrap.

G F Bertsch1, Derek Bingham2

  • 1Department of Physics and Institute of Nuclear Theory, University of Washington, Box 351560, Seattle, Washington 98195, USA.

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Summary
This summary is machine-generated.

The frequency-domain bootstrap (FDB) method efficiently estimates modeling parameter uncertainties, accounting for error correlations. This approach provides more conservative uncertainty estimates than traditional methods, particularly for nuclear physics models.

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Area of Science:

  • Nuclear Physics
  • Computational Modeling
  • Statistical Analysis

Background:

  • Estimating uncertainties in computational models is crucial, especially when modeling errors are significant.
  • Traditional methods like standard bootstrap or chi-squared analysis may not fully capture error correlations.
  • Bayesian methods, while powerful, can be computationally intensive for model calibration.

Purpose of the Study:

  • To introduce and validate the frequency-domain bootstrap (FDB) as a robust method for estimating modeling parameter uncertainties.
  • To demonstrate the FDB's capability in handling error correlations, a limitation in simpler methods.
  • To compare the FDB's performance against existing techniques like chi-squared analysis and Bayesian estimation.

Main Methods:

  • The frequency-domain bootstrap (FDB) technique is proposed for uncertainty estimation.
  • The method's ability to incorporate correlations between modeling errors is highlighted.
  • Computational efficiency is compared to Gaussian process Bayesian estimation.

Main Results:

  • The FDB provides a more conservative estimate of uncertainty for liquid drop model parameters compared to the chi-squared method.
  • Results from the FDB show fair agreement with empirical estimates.
  • The FDB method is shown to be significantly faster than typical Gaussian process Bayesian approaches.

Conclusions:

  • The FDB is an effective and efficient tool for estimating uncertainties in computational models, especially when modeling errors are substantial.
  • The method's ability to handle error correlations makes it superior to simpler techniques.
  • The FDB shows promise for application in advanced nuclear physics models, including those based on density-functional theory.