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Related Concept Videos

Uncertainty: Confidence Intervals00:54

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 't,' or...
Propagation of Uncertainty from Systematic Error01:10

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 particular...
Propagation of Uncertainty from Random Error00:59

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: Overview00:59

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.
Prediction Intervals01:03

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. 
The...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...

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Related Experiment Video

Updated: May 7, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Characterizing and visualizing predictive uncertainty in numerical ensembles through Bayesian model averaging.

Luke Gosink1, Kevin Bensema, Trenton Pulsipher

  • 1Pacific Northwest National Laboratory.

IEEE Transactions on Visualization and Computer Graphics
|September 21, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a novel visual strategy to quantify predictive uncertainty in numerical ensemble forecasts. The method enhances risk analysis by assessing both global and local ensemble performance against observations.

Related Experiment Videos

Last Updated: May 7, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Area of Science:

  • Computational science
  • Data visualization
  • Statistical modeling

Background:

  • Numerical ensemble forecasts are crucial for risk analysis and decision-making in various fields.
  • Assessing the predictive uncertainty of these ensembles is vital for reliable outcomes.

Purpose of the Study:

  • To present a new visual strategy for quantifying and characterizing predictive uncertainty in numerical ensembles.
  • To enable modelers to better evaluate ensemble and individual model performance.

Main Methods:

  • Employing a Bayesian framework to create a statistical aggregate from the ensemble.
  • Extending the aggregate with a visualization strategy to assess uncertainty at global and local levels.
  • Validating the approach using two distinct datasets.

Main Results:

  • The proposed strategy effectively quantifies predictive uncertainty in numerical ensembles.
  • It allows for a nuanced assessment of ensemble and constituent model accuracy and consistency.
  • Demonstrated broad applicability across different datasets.

Conclusions:

  • The new visual strategy enhances the assessment of numerical ensemble forecasting reliability.
  • Improved understanding of predictive uncertainty supports more robust risk analysis and decision-making.
  • The method offers a valuable tool for modelers evaluating forecasting systems.