Optimal upper bounds for non-negative parameters
Fyodor V. Tkachov
TL;DR
This paper improves upper bounds for non-negative parameters at specific confidence levels by incorporating prior information, clarifies a paradox in confidence intervals, and discusses lossless presentation options.
Contribution
It introduces an optimal modification technique for confidence bounds considering non-negativity and clarifies related paradoxes.
Findings
Upper bounds are optimally adjusted for non-negative parameters.
A paradox in confidence intervals at the same confidence level is explained.
A lossless method for presenting confidence results is proposed.
Abstract
Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different confidence intervals for the same confidence level is clarified. The "lossy compression" nature of the device of confidence intervals is discussed and a "lossless" option to present results is pointed out.
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Taxonomy
TopicsParticle physics theoretical and experimental studies · Radioactive Decay and Measurement Techniques · Quantum Mechanics and Applications