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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

Propagation of Uncertainty from Systematic Error

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...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

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...

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

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...

The Uncertainty Principle

The Uncertainty Principle

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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Related Experiment Video

Updated: Jul 26, 2025

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

Characterizing Uncertainty in Machine Learning for Chemistry.

Esther Heid^1,2, Charles J McGill^1,3, Florence H Vermeire^1,4

¹Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.

Journal of Chemical Information and Modeling

|June 20, 2023

Summary

Understanding machine learning uncertainty is key for reliable AI. This study separates data noise (aleatoric) from model limitations (epistemic) to improve chemical property predictions.

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Area of Science:

Computational chemistry
Machine learning reliability
Artificial intelligence in science

Background:

Characterizing uncertainty in machine learning (ML) models is crucial for reliability, robustness, safety, and active learning.
Total uncertainty can be decomposed into aleatoric (data noise) and epistemic (model shortcomings) contributions.
Epistemic uncertainty can be further divided into model bias and variance.

Purpose of the Study:

To systematically analyze the influence of noise, model bias, and model variance on chemical property predictions.
To identify distinct sources of prediction error in diverse chemical spaces.
To develop guidelines for improving underperforming ML models based on their uncertainty context.

Main Methods:

Decomposition of total uncertainty into aleatoric and epistemic components (bias and variance).
Controlled experiments on molecular property datasets.
Analysis of ML model performance concerning data noise, dataset size, model architecture, molecule representation, ensemble size, and data splitting.

Main Results:

Noise in the test set can mask a model's true performance.
Size-extensive model aggregation is vital for predicting extensive properties.
Ensembling effectively quantifies and improves model variance uncertainty.

Conclusions:

Different sources of prediction error significantly impact ML models in distinct ways and require tailored solutions.
Understanding and addressing specific uncertainty contributions is essential for developing robust chemical property prediction models.
General guidelines are provided for model improvement across various uncertainty contexts.