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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.

Shape and Texture of Coarse Aggregate

Shape and Texture of Coarse Aggregate

Aggregate shape is classified based on the relative sharpness or roundness of the edges and corners. This classification includes categories like rounded, angular, elongated, and flaky, each with specific characteristics. Rounded aggregates, fully shaped by attrition, are typical of river or seashore gravel, while angular aggregates, such as crushed rock, have well-defined edges. Aggregates that are elongated and flaky are less desirable, as they can reduce the workability and strength of...

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...

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Related Experiment Video

Updated: Nov 10, 2025

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

Uncertain-DeepSSM: From Images to Probabilistic Shape Models.

Jadie Adams^1,2, Riddhish Bhalodia^1,2, Shireen Elhabian^1,2

¹Scientific Computing and Imaging Institute, University of Utah, UT, USA.

Shape in Medical Imaging : International Workshop, Shapemi 2020, Held in Conjunction with MICCAI 2020, Lima, Peru, October 4, 2020, Proceedings

|April 5, 2021

Summary

This summary is machine-generated.

Uncertain-DeepSSM quantifies shape estimation uncertainty in deep learning models. This approach improves accuracy and trustworthiness for clinical applications, unlike previous overconfident methods.

Keywords:

Bayesian Deep Learning Statistical Shape Modeling Uncertainty Quantification

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Area of Science:

Medical image analysis
Deep learning in medical imaging
Statistical shape modeling

Background:

Statistical shape modeling (SSM) traditionally requires extensive manual segmentation and registration.
Deep learning approaches like DeepSSM automate SSM but often produce overconfident predictions.
Quantifying uncertainty is crucial for clinical trust and reliable diagnostic tools.

Purpose of the Study:

To develop a unified model, Uncertain-DeepSSM, for quantifying uncertainty in deep learning-based SSM.
To improve the trustworthiness of shape estimations for clinical applications.
To enhance the accuracy of SSM while retaining the efficiency of end-to-end deep learning.

Main Methods:

Proposed Uncertain-DeepSSM, a unified model integrating aleatoric and epistemic uncertainty quantification.
Incorporated data-dependent aleatoric uncertainty by adapting the network to predict input variance.
Utilized Monte Carlo dropout sampling for model-dependent epistemic uncertainty estimation.

Main Results:

Uncertain-DeepSSM demonstrated improved accuracy compared to the original DeepSSM.
The model successfully quantified both aleatoric and epistemic uncertainties.
Maintained the end-to-end nature and minimal pre-processing benefits of DeepSSM.

Conclusions:

Uncertain-DeepSSM provides a more trustworthy and accurate approach to statistical shape modeling using deep learning.
Quantifying uncertainty is essential for the clinical translation of deep learning-based medical image analysis tools.
The proposed method enhances diagnostic reliability by indicating the confidence of shape estimations.