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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

2.5K
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. 
2.5K
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

8.7K
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...
8.7K
Confidence Intervals01:21

Confidence Intervals

9.1K
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...
9.1K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

9.9K
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...
9.9K
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

7.6K
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...
7.6K
Confidence Coefficient01:24

Confidence Coefficient

9.1K
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...
9.1K

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Related Experiment Videos

Fast time-series prediction using high-dimensional data: evaluating confidence interval credibility.

Yoshito Hirata1

  • 1Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
PubMed
Summary
This summary is machine-generated.

A new index assesses the trustworthiness of predictions from high-dimensional time-series data. This method measures how far the current state is from the data

Related Experiment Videos

Area of Science:

  • Complex Systems Science
  • Data Science
  • Time Series Analysis

Background:

  • High-dimensional time-series data present challenges in predicting future observables.
  • Evaluating the credibility of confidence intervals in these predictions is crucial for reliable forecasting.
  • Existing methods may not adequately capture the complexity of data manifolds in high-dimensional spaces.

Purpose of the Study:

  • To introduce a novel index for assessing the credibility of confidence intervals for future observables.
  • To provide a quantitative measure of prediction reliability in high-dimensional time-series analysis.
  • To establish a method for evaluating the distance from the current state to the data manifold.

Main Methods:

  • Development of a new credibility index.
  • Calculation of the distance from the current state to the data manifold.
  • Validation using artificial datasets from the Lorenz'96 II and Lorenz'96 I models.

Main Results:

  • Demonstration of the proposed index's utility with complex dynamical systems.
  • The index effectively quantifies the relationship between state-space geometry and prediction credibility.
  • Successful application to artificial datasets generated from Lorenz models.

Conclusions:

  • The proposed index offers a robust method for evaluating confidence interval credibility in high-dimensional time-series.
  • Measuring distance to the data manifold provides valuable insights into prediction uncertainty.
  • This approach enhances the reliability of forecasts in complex systems.