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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Propagation of Uncertainty from Systematic Error

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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...

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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...

The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

Molecular Models

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Updated: Feb 17, 2026

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

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Published on: September 7, 2019

Statistical Framework for Uncertainty Quantification in Computational Molecular Modeling.

Muhibur Rasheed¹, Nathan Clement¹, Abhishek Bhowmick¹

¹Department of Computer Science, University of Texas at Austin, Austin, TX, 78705.

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|December 5, 2017

Summary

This summary is machine-generated.

This study introduces a statistical framework to quantify uncertainty in computational molecular modeling. It provides methods to bound and visualize errors, enhancing the reliability of predictions in biomedical applications.

Keywords:

Molecular Modeling Sampling Uncertainty Quantification

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Published on: April 12, 2019

Area of Science:

Computational biology
Biophysics
Statistical modeling

Background:

Computational modeling is crucial in biomedical research.
Current tools lack rigorous uncertainty quantification for molecular modeling.
Input data in molecular modeling is often noisy or incomplete.

Purpose of the Study:

To develop a statistical framework for quantifying uncertainty in computational molecular modeling.
To express uncertainty as the probability of deviation from the true value.
To improve the reliability of predictions in biomedical pipelines.

Main Methods:

Developed a statistical framework to bound uncertainty using Azuma-Hoeffding inequalities.
Empirically approximated uncertainty by sampling input uncertainties.
Applied the framework to common molecular modeling quantities of interest (QOIs).

Main Results:

The framework provides theoretical bounds on uncertainty probabilities.
Empirical approximation of uncertainty is feasible through input sampling.
Demonstrated application to various QOIs in molecular modeling.

Conclusions:

The developed framework enhances the reliability of computational protocols in molecular modeling.
Provides methods for bounding and visualizing uncertainties in QOIs.
Addresses the critical need for rigorous uncertainty quantification in biomedical predictions.