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...
Saved in:
| Main Authors: | , , , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846112910150991872 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-3d5b033ce5e94ebbbd24fc5384fc644b |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| 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 |
| work_keys_str_mv | AT markncostantini acriticalstudyofthemontecarloreplicamethod AT maevemadigan acriticalstudyofthemontecarloreplicamethod AT lucamantani acriticalstudyofthemontecarloreplicamethod AT jamesmmoore acriticalstudyofthemontecarloreplicamethod AT markncostantini criticalstudyofthemontecarloreplicamethod AT maevemadigan criticalstudyofthemontecarloreplicamethod AT lucamantani criticalstudyofthemontecarloreplicamethod AT jamesmmoore criticalstudyofthemontecarloreplicamethod |