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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Characterization of Parameter Uncertainty in Global Analysis for Ultrafast Spectroscopy Using Markov Chain Monte

Sullivan Bailey-Darland1, Logan S Lancaster1, Taylor D Krueger1

  • 1Department of Chemistry, Oregon State University, 153 Gilbert Hall, Corvallis, Oregon 97331, United States.

Precision Chemistry
|June 1, 2026
PubMed
Summary

Accurate uncertainty analysis in ultrafast spectroscopy is crucial for understanding chemical reactions. This study introduces Markov chain Monte Carlo (MCMC) sampling to improve kinetic parameter uncertainty estimation in global analysis.

Keywords:
Markov chain Monte Carlo samplingerror analysismolecular dynamicsparameter uncertaintytransient absorptionultrafast spectroscopy

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Area of Science:

  • Chemical Dynamics
  • Spectroscopy
  • Computational Chemistry

Background:

  • Ultrafast spectroscopy provides atomic and temporal precision for studying chemical reactions.
  • Kinetic analysis, particularly global analysis, offers insights into chemical system behavior.
  • Accurate uncertainty estimation of kinetic parameters is vital for mechanistic interpretation but often underestimated.

Purpose of the Study:

  • To implement and validate Markov chain Monte Carlo (MCMC) sampling for improved uncertainty analysis in ultrafast spectroscopy data.
  • To develop a procedure for integrating MCMC uncertainty estimation into existing global analysis software.
  • To demonstrate the effectiveness of the MCMC approach on both simulated and experimental femtosecond transient absorption data.

Main Methods:

  • Global analysis of ultrafast spectroscopic data.
  • Markov chain Monte Carlo (MCMC) sampling for parameter uncertainty estimation.
  • Application to femtosecond transient absorption spectroscopy datasets.

Main Results:

  • The MCMC method provides a more reliable estimation of kinetic parameter uncertainty compared to traditional methods.
  • The developed procedure is readily integrable into current spectroscopic analysis software.
  • Parameter uncertainties were found to be within 10% for typical datasets with adequate signal-to-noise ratios.

Conclusions:

  • Markov chain Monte Carlo (MCMC) sampling significantly enhances the accuracy of uncertainty estimation in global analysis of ultrafast spectroscopy data.
  • Simultaneous spectral data collection across multiple wavelengths is essential for precise parameter estimation.
  • The improved uncertainty quantification facilitates more robust mechanistic understanding of chemical processes.