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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2409.11379 |
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| _version_ | 1866912032001884160 |
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| author | Christ, Norman Eranki, Rajiv Kelly, Christopher |
| author_facet | Christ, Norman Eranki, Rajiv Kelly, Christopher |
| contents | We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p-value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling $T^2$ methods based on the conventional $χ^2$ statistic do not apply, such as for uncorrelated fits. Specifically, we analyze a general alternative to the correlated $χ^2$ statistic referred to as $q^2$, and show how to use the bootstrap as a data-driven method to determine the expected distribution of $q^2$ for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p-value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p-value of estimating population parameters from a single ensemble of $N$ samples. The overall method is accurate up to a $1/N$ bias which we do not attempt to quantify. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bootstrap-determined p-values in Lattice QCD Christ, Norman Eranki, Rajiv Kelly, Christopher High Energy Physics - Lattice We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p-value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling $T^2$ methods based on the conventional $χ^2$ statistic do not apply, such as for uncorrelated fits. Specifically, we analyze a general alternative to the correlated $χ^2$ statistic referred to as $q^2$, and show how to use the bootstrap as a data-driven method to determine the expected distribution of $q^2$ for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p-value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p-value of estimating population parameters from a single ensemble of $N$ samples. The overall method is accurate up to a $1/N$ bias which we do not attempt to quantify. |
| title | Bootstrap-determined p-values in Lattice QCD |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2409.11379 |