A background-free counting experiment observes events and wants the 90 per cent…

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Error, Chance and the Machine, Ch Tests, intervals and Bayesian inference

Problem

A background-free counting experiment observes n=2n=2 events and wants the 90 per cent confidence-level Neyman upper limit on the true mean μ\mu of the Poisson count. Someone argues: "The upper limit solves e−μ=αe^{-\mu}=\alpha, so with α=0.10\alpha = 0.10, μup=ln⁡(1/0.10)=2.303\mu_{\rm up} = \ln(1/0.10) = 2.303. There is therefore a 90 per cent probability that the true mean lies below 2.303." Find the error or errors in this argument and give the correct 90 per cent upper limit.

Browse the problem library