# Feldman and Cousins Unified Confidence Intervals

Feldman and Cousins unified confidence belt and lower and upper limit for the parameter mu as a function of the Gaussian-distributed observation x. CLs upper limits are shown for comparison.

One way to characterize the results of a measurement is to quote a frequentist confidence interval for a measured parameter. In many cases the parameter, call it $$\mu$$, is known or expected to be positive, $$\mu\ge 0$$. In a landmark article (and preprint), Feldman and Cousins proposed using a likelihood-ordering principle in order to enable the automatic transition from 1-sided upper limits to 2-sided confidence intervals for the case  $$\mu\ge 0$$, while maintaining the coverage properties of the specified confidence level (CL), i.e., that the published interval has a $$CL$$ probability of containing the true value, independent of the true value.

In this html output of a MATLAB live-script I demonstrate how the Feldman and Cousins procedure is applied to the case of determining the confidence interval of the mean parameter of a (unit) gaussian distribution based on an observation. I reproduce some of the results in their article. The MATLAB live-script is also available.

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Published Mar. 26, 2021 11:28 AM - Last modified Mar. 26, 2021 11:28 AM