Probability Matching Priors in LHC Physics: A Pragmatic Approach
Presented by Mr. Paul BAINES
Probability matching priors (PMP's) provide a bridge between Bayesian and Frequentist inference by yielding Bayesian posterior intervals with Frequentist validity. PMP's also allow the Frequentist access to the powerful computational tools of Bayesian methodology. Unfortunately, such priors are, in general, extremely challenging to implement as they are defined as the solution to a potentially high-dimensional and highly non-linear PDE. Outside the orthogonal case, no general framework exists for the implementation of PMP's. Recent work by Levine & Casella (2003), and Sweeting (2005) has made progress in this area, although neither approach can be applied in full generality. We consider implementation of a PMP for the three Poisson system arising in LHC experiments (as per 'The Banff Challenge', to be presented by Joel Heinrich). In this example, 'approximate probability matching' priors are sought by applying the class of priors from Tibshirani (1989). While derived as first order matching priors for orthogonal parameterizations, we propose applying prior distributions of this form to the non-orthogonal setting. An orthogonality metric is introduced to determine suitability, and relative information surfaces are used to understand the underlying structure of the problem. Simulation results and coverage properties are presented, together with comparison to a variety of alternative Bayesian techniques.