Frequentist-Bayes Hybrid Covariance Estimationfor Unfolding Problems

Abstract

In this paper we present a frequentist-Bayesian hybrid method for estimating covariances of unfolded distributions using pseudo-experiments. The method is compared with other covariance estimation methods using the unbiased Rao-Cramer bound (RCB) and frequentist pseudo-experiments. We show that the unbiased RCB method diverges from the other two methods when regularization is introduced. The new hybrid method agrees well with the frequentist pseudo-experiment method for various amounts of regularization. However, the hybrid method has the added advantage of not requiring a clear likelihood definition and can be used in combination with any unfolding algorithm that uses a response matrix to model the detector response.