A new Monte Carlo-based fitting method

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.

27 pages, 20 figures, 7 tables; final version accepted for publication in J. Phys.G

References in corpus (5)

• Proton spin polarizabilities from polarized Compton scattering
• Dispersion Theory in Electromagnetic Interactions
• Thermonuclear fusion rates for tritium + deuterium using Bayesian methods
• Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method
• First extraction of the scalar proton dynamical polarizabilities from real Compton scattering data

Cited by in corpus (2)

• The valence quark, sea, and gluon content of the pion from the parton distribution functions and the electromagnetic form factor
• First concurrent extraction of the leading-order scalar and spin proton polarizabilities