Statistical and systematical errors in analyses of separate experimental data sets in high energy physics

TL;DR

This paper compares frequentist and Bayesian methods for parameter estimation in high energy physics experiments, highlighting differences in error treatment and proposing an optimal maximum-likelihood approach based on analysis of simulated and real data.

Contribution

It introduces a maximum-likelihood method for combining experimental data, analyzing systematic errors, and compares frequentist and Bayesian approaches in high energy physics.

Findings

Frequentist approach yields larger chi-squared values than Bayesian.

Bayesian method uses Gaussian priors for systematic errors.

Maximum-likelihood method effectively combines data from multiple experiments.

Abstract

Different ways of extracting parameters of interest from combined data sets of separate experiments are investigated accounting for the systematic errors. It is shown, that the frequentist approach may yield larger $\chi^2$ values when compared to the Bayesian approach, where the systematic errors have a Gaussian distributed prior calculated in quadrature. The former leads to a better estimation of the parameters. A maximum-likelihood method, applied to different "gedanken" and real LHC data, is presented. The results allow to choose an optimal approach for obtaining the fit based model parameters.