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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.

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...

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 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 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: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

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Related Experiment Video

Updated: Jul 20, 2025

Watershed Planning within a Quantitative Scenario Analysis Framework

Watershed Planning within a Quantitative Scenario Analysis Framework

Published on: July 24, 2016

A general framework for quantifying uncertainty at scale.

Ionuţ-Gabriel Farcaş¹, Gabriele Merlo¹, Frank Jenko^1,2,3

¹Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX USA.

Communications Engineering

|July 31, 2023

Summary

This summary is machine-generated.

A new adaptive sparse grid interpolation method enables efficient uncertainty quantification and sensitivity analysis for complex computational models. This approach significantly reduces computational cost, making large-scale analysis feasible in scientific research.

Keywords:

Computational science Magnetically confined plasmas

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Area of Science:

Computational science
Plasma physics
Fusion energy research

Background:

Complex computational models are prevalent in science but require significant computational resources.
Limited computational power restricts uncertainty quantification and sensitivity analysis.
Analyzing turbulent transport in magnetic confinement fusion devices is computationally intensive.

Purpose of the Study:

To introduce a novel sensitivity-driven dimension-adaptive sparse grid interpolation strategy.
To enable efficient and accurate uncertainty quantification and sensitivity analysis for computationally expensive models.
To demonstrate the method's efficacy in fusion research.

Main Methods:

Developed a sensitivity-driven dimension-adaptive sparse grid interpolation strategy.
Exploited model structure (intrinsic dimensionality, anisotropic coupling) via adaptivity.
Applied the method to turbulent transport in a magnetic confinement tokamak with eight uncertain parameters.

Main Results:

Reduced computational effort by at least two orders of magnitude for uncertainty quantification and sensitivity analysis.
Achieved an accurate surrogate model that is nine orders of magnitude cheaper than the high-fidelity model.
Demonstrated the efficiency and scalability of the adaptive approach.

Conclusions:

The sensitivity-driven adaptive sparse grid method significantly enhances the feasibility of uncertainty quantification and sensitivity analysis for complex models.
This approach offers substantial computational savings, particularly in demanding fields like fusion research.
The developed surrogate model provides a highly efficient tool for future investigations.