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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

11.8K
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...
11.8K
Confidence Intervals01:21

Confidence Intervals

10.9K
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
10.9K
End Point Prediction: Gran Plot01:07

End Point Prediction: Gran Plot

1.3K
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...
1.3K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.5K
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...
1.5K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

2.0K
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...
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Related Experiment Video

Updated: Feb 25, 2026

Surface Renewal: An Advanced Micrometeorological Method for Measuring and Processing Field-Scale Energy Flux Density Data
09:55

Surface Renewal: An Advanced Micrometeorological Method for Measuring and Processing Field-Scale Energy Flux Density Data

Published on: December 12, 2013

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Empirical prediction intervals improve energy forecasting.

Lynn H Kaack1, Jay Apt2, M Granger Morgan2

  • 1Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213; kaack@cmu.edu.

Proceedings of the National Academy of Sciences of the United States of America
|August 2, 2017
PubMed
Summary
This summary is machine-generated.

Accurate energy projection uncertainty is crucial for policy and investment. A Gaussian density model, estimated on past errors, provides reliable uncertainty estimates for the Annual Energy Outlook (AEO), outperforming existing methods.

Keywords:
continuous ranked probability scoredensity forecastsfan chartforecast uncertaintyscenarios

Related Experiment Videos

Last Updated: Feb 25, 2026

Surface Renewal: An Advanced Micrometeorological Method for Measuring and Processing Field-Scale Energy Flux Density Data
09:55

Surface Renewal: An Advanced Micrometeorological Method for Measuring and Processing Field-Scale Energy Flux Density Data

Published on: December 12, 2013

9.3K

Area of Science:

  • Energy economics
  • Forecasting methodologies
  • Statistical modeling

Background:

  • Energy projections, such as the US Energy Information Administration's Annual Energy Outlook (AEO), are vital for decision-making.
  • Past analyses reveal significant deviations between AEO projections and observed values, highlighting the need for robust uncertainty quantification.

Purpose of the Study:

  • To evaluate the out-of-sample forecasting performance of empirical density forecasting methods for energy quantities.
  • To assess the accuracy of uncertainty estimates in energy projections.
  • To provide guidance on producing, evaluating, and ranking probabilistic forecasts.

Main Methods:

  • Utilized the continuous ranked probability score (CRPS) to evaluate forecasting performance.
  • Assessed a Gaussian density, estimated on historical forecasting errors.
  • Proposed a log transformation for price forecast errors and a modified nonparametric empirical density method.

Main Results:

  • A Gaussian density, estimated on past errors, yielded accurate uncertainty estimates for various AEO energy quantities.
  • This Gaussian approach outperformed the scenario projections offered within the AEO.
  • Probabilistic uncertainties were quantified for 18 core quantities in the AEO 2016 projections.

Conclusions:

  • Gaussian density estimation on past errors is a reliable method for quantifying uncertainty in energy projections.
  • The proposed methods offer improvements for evaluating and communicating uncertainty in energy outlooks.
  • Findings provide practical guidance for enhancing the reliability of future energy forecasts and decision-making.