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Confidence Intervals

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...

Prediction Intervals

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...

Interpretation of Confidence Intervals

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 Intervals

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 Coefficient

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...

Confidence Interval for Estimating Population Mean

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...

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Related Experiment Video

Updated: Jun 23, 2026

Memorization-Based Training and Testing Paradigm for Robust Vocal Identity Recognition in Expressive Speech Using Event-Related Potentials Analysis

Memorization-Based Training and Testing Paradigm for Robust Vocal Identity Recognition in Expressive Speech Using Event-Related Potentials Analysis

Published on: August 9, 2024

Behavior detection using confidence intervals of hidden Markov models.

Richard R Brooks¹, Jason M Schwier, Christopher Griffin

¹The Holcombe Department of Electrical and Computer Engineering, Clemson University, Clemson, SC 29634, USA. rrb@acm.org

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|May 6, 2009

Summary

This study introduces a new method for Hidden Markov Models (HMMs) pattern recognition that uses confidence intervals and receiver operating characteristic curves. This approach improves accuracy by considering data sample size, outperforming existing techniques.

Related Experiment Videos

Last Updated: Jun 23, 2026

Memorization-Based Training and Testing Paradigm for Robust Vocal Identity Recognition in Expressive Speech Using Event-Related Potentials Analysis

Memorization-Based Training and Testing Paradigm for Robust Vocal Identity Recognition in Expressive Speech Using Event-Related Potentials Analysis

Published on: August 9, 2024

Area of Science:

Computer Science
Statistics
Machine Learning

Background:

Markov models and Hidden Markov Models (HMMs) are widely used for analyzing problems with discrete states and stochastic transitions.
Current HMM pattern recognition relies on maximum-likelihood, which has drawbacks including ignoring data sample size and lacking criteria for HMM-data stream matching.

Purpose of the Study:

To develop a novel approach for recognizing complex behaviors using HMMs and confidence intervals.
To address the limitations of maximum-likelihood in HMM pattern recognition, particularly concerning data sample size and model adequacy assessment.

Main Methods:

Utilizing confidence intervals to enhance the certainty of data matches with HMMs, directly correlating certainty with the number of data samples.
Employing receiver operating characteristic (ROC) curves to establish optimal thresholds for accepting or rejecting HMM descriptions.
Applying the proposed method to a family of HMMs and a database of consumer purchase models.

Main Results:

Demonstrated improved accuracy in pattern recognition by incorporating confidence intervals and ROC analysis.
Showcased the utility of the approach through an example using a family of HMMs.
Provided evidence of superior performance compared to existing techniques using a consumer purchase database example.

Conclusions:

The proposed method enhances HMM pattern recognition by integrating confidence intervals and ROC analysis, leading to more reliable assessments of data-model fit.
This approach offers a robust criterion for evaluating HMM adequacy, outperforming traditional maximum-likelihood methods, especially when considering data volume.