Objectively derived default "prior " depends on stopping rule; Bayesian treatment of nuisance parameters is defended.
George Kahrimanis · 2002
Several previous attempts (mine, too) for definingobjective priors have been ineffectual, on account of both unsure derivation and implausible results. In a matter-of-fact approach, the existence of a default “prior ” probability density is established in a special case: if the experimental error, as a random variable, is known, independent of the true value. This findingis extended to the generic case. The resulting “prior ” is the same as the one proposed by V. Balasubramanian (1996), following Jeffreys’ finalapproach. Consequently, prejudice can be eliminated in Bayesian analysis. This prior-free posterior also has a consistent frequentist interpretation. This assessment calls for a review of comparison of Bayesian to frequentist methods. Only the Bayesian method is suitable for obtaining results from atypical data sets. Still, the comparison between classical and Bayesian results can point out for us that the sensitivity of an experiment may need enhancement in a certain range. (Alternatively, one can compute a classical goodness of fit,in this way also testing the plausibility of the model.) Although useful, the classical approach has certain severe side effects, such as coupling of the background with the measured signal even if no events are recorded, and the counterintuitive lowering of upper limits in the presence of systematic uncertainties. Remedies have existed for years, though not yet endorsed by everybody: these side effects have been suppressed by means of a mixed approach, in which the background and/or the systematic uncertainties are treated in a Bayesian fashion. Such mixing is defended again here, with the rationale that normally our beliefs regarding systematic variables and the background are far from controversial (unlike beliefs concerning the estimated variables) therefore a Bayesian treatment is suitable.