1. 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

2. 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

3. 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