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Time-of-flight measurements such as the OPERA and MINOS experiments relycrucially on statistical analysis (as well as many other ingredients) for theirconclusions. The nature of these experiments leads to a simple class ofstatistical models for the results; however, which model in the class isappropriate is not known exactly, as this depends on information obtainedexperimentally, which is subject to noise and other errors. To obtain robustconclusions, this problem, known as "model uncertainty," needs to be addressed,with quantitative bounds on the effect such uncertainty may have on the finalresult.  The OPERA (and MINOS) analysis appears to take steps to mitigate the effectsof model uncertainty, though without quantifying any remaining effect. Wedescribe one of the strategies used (averaging individual probabilitydistributions), and point out a potential source of error if this is notcarried out correctly. We then argue that the correct version of this strategyis not the most effective, and suggest possible alternatives. Thesealternatives may give more accurate statistical results using the same data,allowing, for example, more accurate determination of the dependence of theanomalous time shift on energy. Which strategies work and how well can only beevaluated with access to the full data.  Whether or not the anomalous result from OPERA turns out to be confirmed, webelieve that techniques such as those presented here may be appropriate for theanalysis of other timing experiments of this type.

Statistical model uncertainty and OPERA-like time-of-flight measurements