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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

3.5K
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. 
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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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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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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...
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End Point Prediction: Gran Plot01:07

End Point Prediction: Gran Plot

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A Gran plot is used to predict the equivalence volume or endpoint of a potentiometric or acid-base titration without reaching the endpoint. Typically, titration data is collected as a function of the titrant's volume up to a point less than the equivalence volume and then transformed into a linear format. The straight line is extended to the x-axis, indicating the necessary titrant volume to achieve the equivalence point.
For potentiometric titration, the Gran plot is created by plotting...
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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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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...
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Related Experiment Videos

Extreme-Aware Time-Series Forecasting via Weak-Label-Guided Mixture of Experts.

Jialou Wang1, Jacob Sanderson1, Wai Lok Woo1

  • 1School of Computer Science, Northumbria University, Newcastle upon Tyne NE1 8ST, UK.

Sensors (Basel, Switzerland)
|March 14, 2026
PubMed
Summary
This summary is machine-generated.

Deep time-series forecasting models struggle with rare extremes. A new weak-label-guided mixture of experts (WL-MoE) improves accuracy for critical events like natural disasters by training specialized models.

Keywords:
extreme-aware time-series forecastingheuristic unsupervised routing clusteringweak-label-guided mixture of experts

Related Experiment Videos

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Data Science

Background:

  • Deep time-series forecasting models excel in average accuracy but fail on rare, high-impact extreme events.
  • Class imbalance in data biases models toward majority patterns, hindering prediction of critical events like natural disasters or power outages.

Purpose of the Study:

  • To develop a novel forecasting approach that reliably predicts rare, high-impact extreme events.
  • To enhance model interpretability and audibility for real-world deployment in critical scenarios.

Main Methods:

  • Introduced a weak-label-guided mixture of experts (WL-MoE) routing inputs to specialized temporal regime models.
  • Implemented a two-stage training curriculum: Stage I uses weak labels for expert specialization, Stage II refines forecasting accuracy.
  • Enabled interpretable routing via expert-usage profiling for model behavior auditing.

Main Results:

  • WL-MoE reduced average Mean Squared Error (MSE) by 7.9% and extreme-case MSE by 23.58% across seven benchmark datasets.
  • In a UK flood forecasting study, WL-MoE decreased all-water MSE by 31.6% and high-water MSE by 35.0%.

Conclusions:

  • Weak-label guidance effectively stabilizes expert specialization, improving reliability for rare extreme events.
  • The WL-MoE approach enhances forecasting accuracy and provides auditable model behavior for critical applications.