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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

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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.
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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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Interpretation of Confidence Intervals01:19

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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.
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Confidence Interval for Estimating Population Mean01:25

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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.
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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...
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Related Experiment Video

Updated: Jan 20, 2026

Confidence Intervals
01:21

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Information dynamics with confidence: Using reservoir computing to construct confidence intervals for

David Darmon1, Christopher J Cellucci2, Paul E Rapp3

  • 1Department of Mathematics, Monmouth University, West Long Branch, New Jersey 07764, USA.

Chaos (Woodbury, N.Y.)
|September 2, 2019
PubMed
Summary
This summary is machine-generated.

We developed a bootstrap method to estimate the precision of information dynamics measures. This approach, using echo state networks, provides reliable confidence intervals for analyzing complex systems like sunspot activity.

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Area of Science:

  • Complex Systems
  • Information Theory
  • Time Series Analysis

Background:

  • Information dynamics quantifies information processing in systems, but estimator precision is often unknown for finite data.
  • Understanding statistical properties of information dynamics estimators is crucial for reliable analysis.

Purpose of the Study:

  • To develop statistically sound confidence intervals for information dynamics parameters.
  • To assess the performance of a novel bootstrap procedure for estimating precision.

Main Methods:

  • Utilized an echo state network (ESN), a type of reservoir computer, as a simulator for bootstrap resampling.
  • Conducted Monte Carlo simulations to evaluate confidence interval coverage and length against a random analog predictor.
  • Applied the method to analyze a time series of sunspot counts.

Main Results:

  • The bootstrap confidence intervals demonstrated nominal or near-nominal coverage for information-dynamic measures.
  • The ESN-based bootstrap intervals showed smaller expected lengths compared to the random analog predictor.
  • Successfully characterized the information dynamics of sunspot count data.

Conclusions:

  • The proposed bootstrap procedure offers a reliable method for quantifying uncertainty in information dynamics estimation.
  • This technique enhances the analysis of complex systems by providing crucial precision estimates.
  • The findings are applicable to diverse fields requiring the analysis of time series data.