Bayesian Treatments of Systematic Uncertainties

Luc Demortier The Rockefeller University, New York, NY 10021, U.S.A. Abstract The standard Bayesian treatment of systematic uncertainties is to integrate out the corresponding nuisance parameters from the joint posterior density for all parameters. We apply this formalism to measurements in which the data cannot distinguish between nuisance parameters and parameters of interest, and show that it leads to posterior densities with undesirable properties. To solve this problem, we propose to introduce correlations between the parameters of interest and the nuisance parameters in the prior, in such a way that the nuisance parameter information does not get updated by the measurement. Finally, we describe a method to replace Bayesian marginalization integrals over nuisance parameters by convolutions over the parameters of interest. Such convolutions are computationally more tractable and provide insight into some useful approximations.