Propagating data noise through the fit: the Monte Carlo replica distribution
- 1University of Cambridge
Abstract
A bstract : The Monte Carlo (MC) replica method quantifies parameter uncertainties in global fits of parton distribution functions (PDFs) and Standard Model Effective Field Theory (SMEFT) Wilson coefficients by fitting a model to many noise-perturbed copies of the data and taking the empirical distribution of the best-fit parameters as the uncertainty. The method reproduces the Bayesian posterior exactly only when the model is linear in its parameters, and departs from it in the nonlinear case. We derive the leading-order distribution the method produces and compare it with the Laplace approximation of the Bayesian posterior: the two differ by a single computable matrix, the residual-weighted Hessian of the model at the best fit, whose sign and magnitude set the over- or under-estimation of the parameter uncertainties. This closed-form expression quantifies when and by how much the MC method departs from Bayesian inference. We illustrate it on two single-parameter examples solvable in closed form and point to its evaluation in full PDF and SMEFT fits as a natural next step.
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BibTeX
@article{costantini2026propagating,
title = {{Propagating data noise through the fit: the Monte Carlo replica distribution}},
author = {Mark N. Costantini},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)246},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)246},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Propagating data noise through the fit: the Monte Carlo replica distribution
AU - Mark N. Costantini
PY - 2026
DA - 2026/10/23
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)246
UR - https://link.springer.com/article/10.1007/JHEP10(2026)246
AB - A bstract : The Monte Carlo (MC) replica method quantifies parameter uncertainties in global fits of parton distribution functions (PDFs) and Standard Model Effective Field Theory (SMEFT) Wilson coefficients by fitting a model to many noise-perturbed copies of the data and taking the empirical distribution of the best-fit parameters as the uncertainty. The method reproduces the Bayesian posterior exactly only when the model is linear in its parameters, and departs from it in the nonlinear case. We derive the leading-order distribution the method produces and compare it with the Laplace approximation of the Bayesian posterior: the two differ by a single computable matrix, the residual-weighted Hessian of the model at the best fit, whose sign and magnitude set the over- or under-estimation of the parameter uncertainties. This closed-form expression quantifies when and by how much the MC method departs from Bayesian inference. We illustrate it on two single-parameter examples solvable in closed form and point to its evaluation in full PDF and SMEFT fits as a natural next step.
SN - 1029-8479
ER -