Statistical methods for combinations of experimental results

The reach of many crucial measurements of the T2K and Belle2 programs is severely limited by the small size of the event samples used. In this scenario, completely common for neutrino and quark flavour experiments, the combination of the statistical information from multiple measurements has significant potential to enhance the physics reach over the bare combination of the final results. Past results combination attempts have typically been conducted on an ad-hoc basis and after the individual measurements and their methodological choices and approximations had been consolidated. This results in suboptimal combinations limiting the statistical power of the outcomes.
Each individual measurement typically involves a large number of estimated parameters: the physics parameters of interest and many nuisance parameters correlated with them. While the former can be reasonably cast in an universal experiment-independent format and treated consistently in combinations, the latter are partly universal and partly experiment-dependent. This leads to a variety of possible options for the approximations and approaches needed to include their effect in the combination.
We propose a systematic and consistent plan for obviating the above pitfalls that consists in:

  • A survey of the Belle2 and T2K physics topics and specific measurements where inter-experiment combinations (with NOvA, LHCb, etc. ) have the potential to lead to significant reach enhancements.
  • A survey of past and present combination efforts aimed at forming a global picture of the variance of the approaches adopted, the approximations made, and the possible pitfalls/inconsistencies encountered.
  • A unified proposal for: (i) restricting the definition of the relevant physics and nuisance parameters for each measurement to one or few variants; (ii) restricting the approximations associated with the modelling of the interplay between nuisance and physics parameters to a few consistent variants. The proposal will be documented in a report that will serve as a reference for experimental groups willing to combine their results, which will be invited to conform to the selected prescriptions.

A possible development of such work could be to set up a software framework (e.g., a data base) explicitly suited and optimized for (i) accepting as inputs the values of multivariate likelihoods from each individual measurement and (ii) operating consistently the combination (likelihood multiplication) taking properly into account the commonalities between physics and global nuisance parameters and treating coherently experiment-dependent nuisance parameters. If successful, this work will enhance the physics reach of the single experiments both in neutrino and quark flavor physics.