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Uncertainty: Confidence Intervals

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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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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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Empirical weighted Bayesian tolerance intervals.

¹Product Quality Management, Janssen Pharmaceuticals, Titusville, New Jersey, USA.

Journal of Biopharmaceutical Statistics

|September 30, 2020

Summary

This summary is machine-generated.

This study introduces an empirical weighted Bayesian tolerance interval (TI) approach. It offers a compromise between existing methods, providing narrower limits while maintaining reliable confidence coverage for quality assurance.

Keywords:

Bayesian tolerance intervals normal tolerance intervals sample size determination two-sided tolerance interval

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Area of Science:

Statistics
Quality Assurance
Bayesian Inference

Background:

Bayesian statistics integrates prior knowledge into statistical inference.
Tolerance intervals (TI) are crucial for product quality assurance.
Existing Bayesian TI methods include Hamada and Wolfinger approaches.

Purpose of the Study:

To compare Hamada, Wolfinger, and frequentist tolerance intervals using simulations.
To address the conservativeness of Hamada TI and the liberality of Wolfinger TI with increasing sample sizes.
To propose a novel empirical weighted Bayesian TI approach.

Main Methods:

Simulation-based comparison of two-sided Wolfinger, Hamada, and frequentist tolerance intervals.
Evaluation of probability content control at specified confidence levels.
Development of an empirical weighted Bayesian TI as a compromise.

Main Results:

Hamada TI become more conservative than frequentist TI as sample size increases.
Wolfinger TI become more liberal than frequentist TI as sample size increases.
The proposed empirical weighted Bayesian TI provides narrower limits in some scenarios.

Conclusions:

The proposed Bayesian TI approach balances the properties of Hamada and Wolfinger methods.
This new approach ensures comparable confidence content coverage to frequentist methods.
It offers an improved statistical tolerance interval for quality assurance applications.