A new Monte Carlo-based fitting method

TL;DR

This paper introduces a bootstrap-based fitting method that improves confidence interval and p-value reliability over traditional methods, especially when systematic uncertainties are significant, demonstrated through toy models and real physics data.

Contribution

The paper presents a novel Monte Carlo-based fitting technique utilizing the parametric bootstrap, enhancing the reliability of statistical inference in the presence of systematic uncertainties.

Findings

Bootstrap method provides reliable confidence intervals and p-values with systematic uncertainties.

Compared to $^2$ minimization and Bayesian approaches, bootstrap yields more accurate uncertainty estimates.

Application to real Compton scattering data confirms the method's effectiveness and portability.

Abstract

We present a new fitting technique based on the parametric bootstrap method, which relies on the idea to produce artificial measurements using the estimated probability distribution of the experimental data. In order to investigate the main properties of this technique, we develop a toy model and we analyze several fitting conditions with a comparison of our results to the ones obtained using both the standard $\chi^2$ minimization procedure and a Bayesian approach. Furthermore, we investigate the effect of the data systematic uncertainties both on the probability distribution of the fit parameters and on the shape of the expected goodness-of-fit distribution. Our conclusion is that, when systematic uncertainties are included in the analysis, only the bootstrap procedure is able to provide reliable confidence intervals and p-values, thus improving the results given by the standard $\chi^2$ minimization approach. Our technique is then applied to an actual physics process, the real Compton scattering off the proton, thus confirming both the portability and the validity of the bootstrap-based fit method.