Frequentist-Bayes Hybrid Covariance Estimationfor Unfolding Problems

TL;DR

This paper introduces a hybrid covariance estimation method combining frequentist and Bayesian approaches for unfolding problems, which is flexible, does not require a likelihood, and aligns well with pseudo-experiment results.

Contribution

A novel hybrid covariance estimation method for unfolding that works without a clear likelihood and is compatible with any unfolding algorithm using a response matrix.

Findings

Hybrid method agrees with pseudo-experiments across regularization levels.

Unbiased RCB diverges when regularization is used.

Hybrid method does not require a likelihood function.

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.