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Related Concept Videos

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...
Confidence Intervals01:21

Confidence Intervals

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 confidence...
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
Confidence Coefficient01:24

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the...

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Related Experiment Videos

Confidence interval prediction for neural network models.

G Chryssolouris1, M Lee, A Ramsey

  • 1Lab. for Manuf. and Productivity, MIT, Cambridge, MA.

IEEE Transactions on Neural Networks
|January 1, 1996
PubMed
Summary
This summary is machine-generated.

Quantifying confidence intervals for neural network models is crucial for understanding their accuracy in modeling physical systems. This study proposes a method that considers training data accuracy and assumes normally distributed errors.

Related Experiment Videos

Area of Science:

  • Computational physics
  • Machine learning applications
  • Statistical modeling

Background:

  • Empirical modeling tools like neural networks are increasingly used for physical systems.
  • Model predictions inherently contain errors due to system complexities and unobservable factors.
  • Quantifying the uncertainty in neural network predictions is essential for reliable scientific application.

Purpose of the Study:

  • To develop a method for estimating confidence intervals of neural network models applied to physical systems.
  • To provide a quantitative measure of accuracy for neural network empirical modeling.
  • To address the challenge of error propagation in complex system modeling.

Main Methods:

  • A novel method to compute confidence intervals for neural network models is proposed.
  • The method assumes normally distributed errors within the neural network.
  • It explicitly incorporates the accuracy of the training data into the confidence interval calculation.

Main Results:

  • The developed method provides a quantifiable estimate of neural network model accuracy.
  • Confidence intervals can be derived by assuming normally distributed errors.
  • Accounting for training data accuracy improves the reliability of the uncertainty estimation.

Conclusions:

  • The proposed method offers a robust way to assess the predictive accuracy of neural networks in physical system modeling.
  • This approach enhances the trustworthiness of neural networks as empirical tools.
  • Further research can explore non-normally distributed error assumptions for broader applicability.