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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 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...

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...

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.

Survival Tree

Survival Tree

Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
Building a Survival Tree
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Related Experiment Video

Updated: Sep 16, 2025

Brain Infarct Segmentation and Registration on MRI or CT for Lesion-symptom Mapping

Brain Infarct Segmentation and Registration on MRI or CT for Lesion-symptom Mapping

Published on: September 25, 2019

Towards reliable WMH segmentation under domain shift: An application study using maximum entropy regularization to

Franco Matzkin¹, Agostina Larrazabal², Diego H Milone¹

¹Institute for Signals, Systems and Computational Intelligence, sinc(i) CONICET-UNL, Santa Fe, Argentina.

Computers in Biology and Medicine

|July 4, 2025

Summary

Maximum-entropy regularization enhances white matter hyperintensity (WMH) segmentation by improving uncertainty estimation. This helps identify segmentation errors in diverse clinical settings without needing ground-truth labels.

Keywords:

Domain shift Maximum-entropy regularization Medical image segmentation Uncertainty estimation White matter hyperintensity

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Area of Science:

Medical imaging analysis
Deep learning for neuroimaging

Background:

Accurate white matter hyperintensity (WMH) segmentation is vital for neurological conditions like multiple sclerosis.
Domain shifts in MRI data (e.g., different machines or parameters) challenge model calibration and uncertainty estimation.
Predictive uncertainty can serve as a proxy to identify post-deployment errors without ground-truth labels.

Purpose of the Study:

To investigate the impact of domain shift on WMH segmentation accuracy.
To evaluate maximum-entropy regularization techniques for enhancing model calibration and uncertainty estimation in WMH segmentation.
To identify potential segmentation errors in clinical deployment using predictive uncertainty.

Main Methods:

Utilized a U-Net architecture for WMH segmentation.
Applied and evaluated maximum-entropy regularization schemes.
Tested on two public datasets: WMH Segmentation Challenge and 3D-MR-MS.
Assessed performance using Dice coefficient, Hausdorff distance, expected calibration error, and entropy-based uncertainty.

Main Results:

Entropy-based uncertainty estimates effectively predict segmentation errors across different data distributions.
Maximum-entropy regularization strengthens the link between uncertainty and segmentation performance.
Model calibration is improved under domain shift conditions.

Conclusions:

Maximum-entropy regularization enhances uncertainty estimation for WMH segmentation, especially under domain shift.
These methods enable reliable flagging of unreliable predictions without ground-truth annotations.
Improved model calibration supports safer deployment of deep learning in heterogeneous clinical environments.