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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.

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 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...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Variation

Variation

An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...

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Updated: Sep 3, 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

Evaluating and Calibrating Uncertainty Prediction in Regression Tasks.

Dan Levi¹, Liran Gispan¹, Niv Giladi^1,2

¹General Motors Israel, Herzliya 4672515, Israel.

Sensors (Basel, Switzerland)

|July 28, 2022

Summary

This summary is machine-generated.

This study introduces a new definition and method for evaluating uncertainty calibration in regression tasks, improving predictions for safety-critical machine learning applications. The proposed approach offers a simple yet effective calibration technique outperforming complex methods.

Keywords:

prediction uncertainty regression

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Last Updated: Sep 3, 2025

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

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An R-Based Landscape Validation of a Competing Risk Model

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Published on: October 23, 2020

Area of Science:

Machine Learning
Computer Vision
Data Science

Background:

Accurate uncertainty prediction is crucial for safety-critical machine learning applications, especially in regression tasks.
Existing definitions for regression uncertainty calibration have limitations in distinguishing informative from non-informative predictions.

Purpose of the Study:

To address limitations in current regression uncertainty calibration definitions.
To propose a novel definition and evaluation method for regression uncertainty calibration.
To introduce a simple, effective calibration technique for regression tasks.

Main Methods:

Developed a new definition for regression uncertainty calibration.
Proposed a histogram-based evaluation method to cluster examples by uncertainty.
Introduced a simple, scaling-based calibration method.

Main Results:

The new definition effectively distinguishes informative from non-informative uncertainty predictions.
The histogram-based evaluation method provides a robust way to assess calibration.
The proposed scaling-based calibration method achieves performance comparable to more complex techniques.
Validated on synthetic data and object detection bounding-box regression (COCO, KITTI datasets).

Conclusions:

The proposed definition and evaluation method offer significant improvements for regression uncertainty calibration.
A simple scaling-based calibration method is effective and practical for real-world applications.
This work enhances the reliability of machine learning models in safety-critical domains.