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SENSOP: a derivative-free solver for nonlinear least squares with sensitivity scaling
I S Chan1, A A Goldstein, J B Bassingthwaighte
1Center for Bioengineering, University of Washington, Seattle 98195.
Annals of Biomedical Engineering
|November 1, 1993
Summary
This study introduces SENSOP, a weighted nonlinear least squares optimizer for complex data fitting. SENSOP effectively handles data with potentially non-constant variance, improving parameter estimation accuracy.
Area of Science:
- Optimization methods
- Statistical modeling
- Signal processing
Background:
- Nonlinear least squares (NLS) optimization is standard for fitting complex models.
- Traditional NLS assumes constant data point variance, limiting its application.
- Real-world data often exhibit non-constant variance, posing challenges for NLS.
Purpose of the Study:
- Introduce SENSOP, a weighted nonlinear least squares (WNLS) optimizer.
- Develop a method for estimating appropriate weighting functions for WNLS.
- Address challenges in parameter estimation for data with wide dynamic ranges.
Main Methods:
- Implemented a variant of the Levenberg-Marquardt algorithm for parameter vector updates.
- Developed a general method for estimating weighting functions applicable to 1D and higher-dimensional signals.
- Utilized a fractional power function for weighting in multi-tracer outflow dilution curves.
Main Results:
- SENSOP successfully fits models to data with non-constant variance.
- The proposed weighting function estimation method is broadly applicable.
- A fractional power weighting function proved effective for wide-range dilution curve data.
Conclusions:
- SENSOP provides a robust solution for nonlinear model fitting with non-constant variance.
- The weighting function estimation technique enhances parameter estimation accuracy.
- WNLS, particularly with fractional power weighting, is effective for challenging datasets like tracer dilution curves.