The observables are counts N, Y, and Z, with

N ~ Pois(ε λ_S + λ_B) ,
Y ~ Pois(ρ λ_B) ,
Z ~ Pois(ε υ) ,

where λ_S is the parameter of interest (in this case, the mass of the Higgs boson, but could be the intensity of a source), λ_B is the parameter that describes the background, ε is the efficiency, or the effective area, of the detector, and υ is a calibrator source with a known intensity.

The challenge was (is) to infer the maximum likelihood estimate of and the bounds on λ_S, given the observed data, {N, Y, Z}. In other words, to compute

p(λ_S|N,Y,Z) .

It may look like an easy problem, but it isn’t!