The Monte Carlo replica method: investigating the effects of non-linearity
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912062488182784 |
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| author | Costantini, Mark N. |
| author_facet | Costantini, Mark N. |
| contents | This paper presents an in-depth mathematical analysis of the Monte Carlo replica method, commonly used in global fitting studies within the high-energy physics theory field. For the first time, we offer a rigorous derivation of the parameter distributions resulting from this method, demonstrating that, while they align with Bayesian posteriors in linear models, they deviate in non-linear cases. We then numerically assess this discrepancy in a phenomenologically important context: fitting SMEFT Wilson coefficients. Our findings reveal that when non-linearity plays a significant role, the uncertainty estimates for key quantities differ between the two approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_05324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Monte Carlo replica method: investigating the effects of non-linearity Costantini, Mark N. High Energy Physics - Phenomenology This paper presents an in-depth mathematical analysis of the Monte Carlo replica method, commonly used in global fitting studies within the high-energy physics theory field. For the first time, we offer a rigorous derivation of the parameter distributions resulting from this method, demonstrating that, while they align with Bayesian posteriors in linear models, they deviate in non-linear cases. We then numerically assess this discrepancy in a phenomenologically important context: fitting SMEFT Wilson coefficients. Our findings reveal that when non-linearity plays a significant role, the uncertainty estimates for key quantities differ between the two approaches. |
| title | The Monte Carlo replica method: investigating the effects of non-linearity |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.05324 |