Bayesian analysis at work troublesome examples J. Charles, A. Hoecker, H. Lacker and F. Le Diberder

Outline Setting the stage Frequentist analysis Bayesian analysis Simplified stage Concerns and Conclusion

Setting the Stage α B decays into π π final states 6 observables And 6 theoretical unknown 6 decay amplitudes are involved CP Violation α

α

Bayesian Analysis α Data Theoretical parameters: mind are random variables - following known PDF mind

Quantum Mechanics parameterization 6 decay amplitudes are involved One phase may be set to zero Bayesian (I) frequentist

Standard model parameterization The 6 amplitudes are split into two kind of contributions Trees & Penguins 10^9 Bayesian (II) amplitudes & phases … or real & Imaginary parts ? Bayesian (II) frequentist Bayesian (III)

Changing decay channel (ρρ) Bayesian (I) Bayesian (II) !?! Quantum Mechanics amplitudes & phases JHEP 0507:028,2005 frequentist (I)(II)(II) real & imaginary parts Bayesian (III)

B → π π Taking key experimental information away removing all experimental hints related to α amplitudes & phases Quantum Mechanics

Conclusion … that attractive ? priors parameterization

Spheres within a cube Simplified Stage 6 D space Bayesian treatment one knows nothing about the individual space components x,y,z… What do we known about the radius r =√(x^2+y^2+…) ?

Concerns & Conclusion α CKM Should we ?