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Updated: Jun 8, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.

H T Banks¹, Kathleen Holm, Danielle Robbins

¹Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine North Carolina State University Raleigh, NC 27695-8212.

Mathematical and Computer Modelling

|September 14, 2010

Summary

This summary is machine-generated.

This study compares bootstrapping and asymptotic theory for uncertainty quantification in nonlinear dynamical systems. Asymptotic theory offers faster computation and more reliable confidence intervals for parameter estimation.

Related Experiment Videos

Last Updated: Jun 8, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Area of Science:

Computational science
Dynamical systems theory
Statistical inference

Background:

Inverse problems are crucial for parameter estimation in dynamical systems.
Uncertainty quantification (UQ) is essential for reliable model predictions.
Nonlinear systems and various noise types present significant challenges in UQ.

Purpose of the Study:

To computationally investigate and compare bootstrapping and asymptotic theory for UQ in nonlinear parameter-dependent dynamical systems.
To evaluate the performance of these methods under different data noise conditions (absolute and relative error).
To contrast parameter estimates, standard errors, confidence intervals, and computational efficiency.

Main Methods:

Development and application of computational frameworks for UQ.
Implementation of bootstrapping and asymptotic theory approaches.
Analysis of parameter estimation accuracy and uncertainty measures.
Comparative assessment of computational performance.

Main Results:

Asymptotic theory generally provides more accurate standard errors and narrower confidence intervals compared to bootstrapping.
Both methods show varying performance depending on noise characteristics (constant vs. non-constant variance).
Asymptotic theory demonstrates superior computational efficiency over bootstrapping.

Conclusions:

Asymptotic theory is a computationally efficient and reliable method for UQ in the specified inverse problems.
The choice of UQ method should consider the nature of data noise.
Further research can explore hybrid approaches or extensions to more complex systems.