A critical study of the Monte Carlo replica method

Abstract We present a detailed mathematical study of the Monte Carlo replica method as applied in the global fitting literature from the high-energy physics theory community. For the first time, we provide a rigorous derivation of the parameter distributions implied by the method, and show that, whi...

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Main Authors: Mark N. Costantini, Maeve Madigan, Luca Mantani, James M. Moore
Format: Article
Language:English
Published: SpringerOpen 2024-12-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP12(2024)064
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author Mark N. Costantini
Maeve Madigan
Luca Mantani
James M. Moore
author_facet Mark N. Costantini
Maeve Madigan
Luca Mantani
James M. Moore
author_sort Mark N. Costantini
collection DOAJ
description Abstract We present a detailed mathematical study of the Monte Carlo replica method as applied in the global fitting literature from the high-energy physics theory community. For the first time, we provide a rigorous derivation of the parameter distributions implied by the method, and show that, whilst they agree with Bayesian posteriors for linear models, they disagree otherwise. We proceed to numerically quantify the disagreement between the Monte Carlo replica method and the Bayesian method in the context of two phenomenologically relevant scenarios: fits of the SMEFT Wilson coefficients, and fits of PDFs (albeit in a toy scenario). In both scenarios, we find that uncertainty estimates of the quantities of interest are discrepant between the two approaches when non-linearity is relevant. Our findings motivate future investigation of Bayesian methodologies for global PDF fits, especially in the context of simultaneous determination of PDFs and SMEFT Wilson coefficients.
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spelling doaj-art-3d5b033ce5e94ebbbd24fc5384fc644b2024-12-22T12:09:46ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241213810.1007/JHEP12(2024)064A critical study of the Monte Carlo replica methodMark N. Costantini0Maeve Madigan1Luca Mantani2James M. Moore3DAMTP, University of CambridgeInstitut für Theoretische Physik, Universität HeidelbergDAMTP, University of CambridgeDAMTP, University of CambridgeAbstract We present a detailed mathematical study of the Monte Carlo replica method as applied in the global fitting literature from the high-energy physics theory community. For the first time, we provide a rigorous derivation of the parameter distributions implied by the method, and show that, whilst they agree with Bayesian posteriors for linear models, they disagree otherwise. We proceed to numerically quantify the disagreement between the Monte Carlo replica method and the Bayesian method in the context of two phenomenologically relevant scenarios: fits of the SMEFT Wilson coefficients, and fits of PDFs (albeit in a toy scenario). In both scenarios, we find that uncertainty estimates of the quantities of interest are discrepant between the two approaches when non-linearity is relevant. Our findings motivate future investigation of Bayesian methodologies for global PDF fits, especially in the context of simultaneous determination of PDFs and SMEFT Wilson coefficients.https://doi.org/10.1007/JHEP12(2024)064Parton DistributionsSMEFT
spellingShingle Mark N. Costantini
Maeve Madigan
Luca Mantani
James M. Moore
A critical study of the Monte Carlo replica method
Journal of High Energy Physics
Parton Distributions
SMEFT
title A critical study of the Monte Carlo replica method
title_full A critical study of the Monte Carlo replica method
title_fullStr A critical study of the Monte Carlo replica method
title_full_unstemmed A critical study of the Monte Carlo replica method
title_short A critical study of the Monte Carlo replica method
title_sort critical study of the monte carlo replica method
topic Parton Distributions
SMEFT
url https://doi.org/10.1007/JHEP12(2024)064
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AT maevemadigan acriticalstudyofthemontecarloreplicamethod
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AT jamesmmoore acriticalstudyofthemontecarloreplicamethod
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AT maevemadigan criticalstudyofthemontecarloreplicamethod
AT lucamantani criticalstudyofthemontecarloreplicamethod
AT jamesmmoore criticalstudyofthemontecarloreplicamethod