Feldman-Cousins Method New method for confidence intervals/limits Improvements compared to Bayesian and classical constructions Unifies upper confidence limit (for null results) and confidence intervals (non-null results) Avoids unphysical confidence intervals Reduces problems with overly biased priors (as in Bayesian) and introduces improved ordering system for classical construction Antonia Hubbard

How it works Construct pdf: P(x|µ) X= observable, µ = true value we’re looking for Measeured x₀ has likelihood function L(x₀, µ) Find u’ that maximizes P(x₀ |µ): P(x₀ |u’) = Pmax Find ratio: R =P(x₀|u)/P(x₀ |µ’) For a given u, add values of x in order of highest R values until sum(P(x|µ)) = C.L. For measured x₀, we now have confidence limits [µ1, µ2] as in classical construction Antonia Hubbard

What to use it on Gaussian with bounded physical region Previous problems with, for example, a result of 2±3 unphysical results New construction implements boundary with a limitation on µ’ Upper limit decreases as 1/|x| for negative x Quickly decreases upper limits Poissonian process with background Low probabilites on absolute scale get better handled with ratio method Helps reduce conservatism from discreetness of n Eliminated “flip flopping” problems between upper limit and intervals Antonia Hubbard